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This paper suggests a novel methodology for building robust information processing systems based on wavelets and artificial neural networks (ANN) to be applied either in decision‐making tasks based on image information or in signal prediction and modeling tasks. The efficiency of such systems is increased when they simultaneously use input information in its original and wavelet transformed form, invoking ANN technology to fuse the two different types of input. A quality control decision‐making system as well as a signal prediction system have been developed to illustrate the validity of our approach. The first one offers a solution to the problem of defect recognition for quality control systems. The second application improves the quality of time series prediction and signal modeling in the domain of NMR. The accuracy obtained shows that the proposed methodology deserves the attention of designers of effective information processing systems.

The purpose of this paper is to examine contagion among the major world markets during the last 25 years and propose a new way to analyze contagion with wavelet methods.

The analysis uses a novel way to study contagion using wavelet methods. The comparison is made between co‐movements at different time scales. Co‐movement methods of the discrete wavelet transform and the continuous wavelet transform are applied.

Clear signs of contagion among the major markets are found. Short time scale co‐movements increase during the major crisis while long time scale co‐movements remain approximately at the same level. In addition, gradually increasing interdependence between markets is found.

Because of the chosen method, the approach is limited to large data sets.

The research has practical implications to portfolio managers etc. who wish to have better view of the dynamics of the international equity markets.

The research uses novel wavelet methods to analyze world equity markets. These methods allow the markets to be analyzed in the whole state space.

The purpose of this paper is to identify significant factors of environmental variables and pollutants that have an effect on PM_2.5 through wavelet and regression analysis.

In order to provide stable data set for regression analysis, multiresolution analysis using wavelets is conducted. For the sampled data, multicollinearity among the independent variables is removed by using principal component analysis and multiple linear regression analysis is conducted using PM_2.5 as a dependent variable.

It is found that few pollutants such as NO₂, NO_x, SO₂, benzene and environmental factors such as ambient temperature, solar radiation and wind direction affect PM_2.5. The regression model developed has high R² value of 91.9 percent, and the residues are stationary and not correlated indicating a sound model.

The research provides a framework for extracting stationary data and other important features such as change points in mean and variance, using the sample data for regression analysis. The work needs to be extended across all areas in India and for various other stationary data sets there can be different factors affecting PM_2.5.

Control measures such as control charts can be implemented for significant factors.

Rules and regulations can be made more stringent on the factors.

The originality of this paper lies in the integration of wavelets with regression analysis for air pollution data.

Fueled by the rapid growth of internet, steganography has emerged as one of the promising techniques in the communication system to obscure the data. Steganography is defined as the process of concealing the data or message within media files without affecting the perception of the image. Media files, like audio, video, image, etc., are utilized to embed the message. Nowadays, steganography is also used to transmit the medical information or diagnostic reports. The paper aims to discuss these issues.

In this paper, the novel wavelet transform-based steganographic method is proposed for secure data communication using OFDM system. The embedding and extraction process in the proposed steganography method exploits the wavelet transform. Initially, the cost matrix is estimated by the following three aspects: pixel intensity, edge transformation and wavelet transform. The cost estimation matrix provides the location of the cover image where the message is to be entrenched. Then, the wavelet transform is utilized to embed the message into the cover image according to the cost value. Subsequently, in the extraction process, the wavelet transform is applied to the embedded image to retrieve the message efficiently. Finally, in order to transfer the secret information over the channel, the newly developed wavelet-based steganographic method is employed for the OFDM system.

The experimental results are evaluated and performance is analyzed using PSNR and MSE parameters and then compared with existing systems. Thus, the outcome of our wavelet transform steganographic method achieves the PSNR of 71.5 dB which ensures the high imperceptibility of the image. Then, the outcome of the OFDM-based proposed steganographic method attains the higher PSNR of 71.07 dB that proves the confidentiality of the message.

In the authors’ previous work, the embedding and extraction process was done based on the cost estimation matrix. To enhance the security throughout the communication system, the novel wavelet-based embedding and extraction process is applied to the OFDM system in this paper. The idea behind this method is to attain a higher imperceptibility and robustness of the image.

The purpose of this paper is to reduce the destructive effects of existing unavoidable noises contaminating temperature data in inverse heat conduction problems (IHCP) utilizing the wavelets.

For noise reduction, sensor data were treated as input to the filter bank used for signal decomposition and implementation of discrete wavelet transform. This is followed by the application of wavelet denoising algorithm that is applied on the wavelet coefficients of signal components at different resolution levels. Both noisy and de‐noised measurement temperatures are then used as input data to a numerical experiment of IHCP. The inverse problem deals with an estimation of unknown surface heat flux in a 2D slab and is solved by the variable metric method.

Comparison of estimated heat fluxes obtained using denoised data with those using original sensor data indicates that noise reduction by wavelet has a potential to be a powerful tool for improvement of IHCP results.

Noise reduction using wavelets, while it can be implemented very easily, may also significantly relegate (or even eliminate) conventional regularization schemes commonly used in IHCP.

This study examines the tracking error (TE) of a sample of sector exchange traded funds (ETFs) using spectral techniques.

TE is examined by computing its power spectrum using the wavelet transform. The wavelet transform maps the TE time series from the time domain to the time–frequency domain. Albeit the wavelet transform is a more complicated mathematical tool compared with the Fourier transform, it also has important advantages such as that it allows to analyze non-stationary data and to detect transient behavior.

Results show that changes in the TE of a sample of sector ETFs are captured by the wavelet transform. Moreover, the authors also find that the wavelet coherence function can be used as a measure of TE in the time–frequency domain.

The study shows that the wavelet coherence function can be used as a reliable measure of TE.

The purpose of this paper is to derive crucial insights from multi-scale analysis to detect equity return co-movements between Korean and emerging Asian markets.

Wavelet correlation, wavelet coherence and wavelet clustering measures are used to uncover Korean equity market interactions which are hard to see using any other modern econometric method and which would otherwise had remained hidden.

The authors observed that Korean equity market is strongly integrated with Asian equity markets at lower frequency scales and has a relatively weak correlation at higher frequencies. Further this correlation eventually grows strong in the interim of crises period at lower frequency scales. The authors, however, do not found any significant deviation in dendrograms generated in data clustering process from wavelet scale 2 to 6 which are associated with four and 64 weeks period, respectively. Overall the findings are relevant and have strong policy and practical implications.

The unique contribution of this paper is that it introduces wavelet clustering analysis to produce a nested hierarchy of similar markets at each frequency level for the first time in finance literature

The purpose of this paper is to propose an efficient computational technique, which uses Haar wavelets collocation approach coupled with the Newton-Raphson method and solves the following class of system of Lane–Emden equations:

To deal with singularity, Haar wavelets are used, and to deal with the nonlinear system of equations that arise during computation, the Newton-Raphson method is used. The convergence of these methods is also established and the results are compared with existing techniques.

The authors propose three methods based on uniform Haar wavelets approximation coupled with the Newton-Raphson method. The authors obtain quadratic convergence for the Haar wavelets collocation method. Test problems are solved to validate various computational aspects of the Haar wavelets approach. The authors observe that with only a few spatial divisions the authors can obtain highly accurate solutions for both initial value problems and boundary value problems.

The results presented in this paper do not exist in the literature. The system of nonlinear singular differential equations is not easy to handle as they are singular, as well as nonlinear. To the best of the knowledge, these are the first results for a system of nonlinear singular differential equations, by using the Haar wavelets collocation approach coupled with the Newton-Raphson method. The results developed in this paper can be used to solve problems arising in different branches of science and engineering.

Interturn winding faults, one of the most important causes of power transformers failures, cannot be detected by existing detection methods until they develop into high‐level faults with more severe damage to the transformer. The purpose of this paper is to describe development of a new discrete wavelet transform (DWT) based approach for detection of winding interturn faults.

The following approach was accomplished for development of the proposed fault detection method in this study. The DWT was first applied to decompose the terminal current signals of a transformer, which in turn were obtained from simulations using a finite elements method model of the transformer, into a series of wavelet components. Based on the characteristic features associated with interturn faults extracted from the decomposed waveforms of the terminal currents, a detection scheme was developed. An experimental setup was used to validate the proposed detection method.

The results of this study demonstrate the efficacy of DWT applied on terminal currents of the transformer to identify interturn faults on the windings well before such faults lead to a catastrophic failure. It is believed that, based on the present findings, there definitely exists scope for improving interturn fault diagnosis with wavelet transform.

Performing more detailed studies to find all relevant characteristics of the wavelet transform in this application, identifying the location of the faulted turns along winding, applying the method for indicating early stages of turn insulation deterioration and evaluating other type of wavelets for this application would be some future directions of this research.

With the proposed method, it is becoming possible to detect early signs of the fault occurrence, so that the necessary corrective actions can be taken to prevent long‐lasting outages and reduce down times of the faulty power transformer. The method will be particularly useful as a complement for the classical protection devices of the power transformers.

Some recent studies have been carried out regarding the application of DWT for discrimination between an internal fault and other disturbances such as magnetizing inrush and external faults. This paper extends those studies for the detection of interturn faults using more quantitative and qualitative characteristics features.

The real challenge in the solution of contact problems is the lack of an optimal adaptive scheme. As the contact zone is a priori unknown, successive refinement and iterative method are necessary to obtain a high-accuracy solution. The purpose of this paper is to provide an optimal adaptive scheme based on second-generation finite element wavelets for the solution of non-linear variational inequality of the contact problem.

To generate an elementary multi-resolution mesh, the authors used hierarchical bases (HB) composed of Lagrange finite element interpolation functions. These HB functions are customized using second-generation wavelet techniques for a fast convergence rate. At each step of the algorithm, the active set method along with mesh adaptation is used for solving the constrained minimization problem of contact case. Wavelet coefficients-based error indicators are used, and computation is focused on mesh zones with a high error indication. The authors take advantage of the wavelet transform to develop a parameter-free adaptive scheme to generate an appropriate and optimal mesh.

Adaptive wavelet Galerkin scheme (AWGS), a newly developed method for multi-scale mesh adaptivity in this work, is a combination of the second-generation wavelet transform and finite element method and significantly improves the accuracy of the results without approximating an additional problem of error estimation equations. A comparative study is performed taking a solution on a highly refined mesh and results are generated using AWGS.

The proposed adaptive technique can be utilized in the simulation of mechanical and biomechanical structures where multiple bodies come into contact with each other. The algorithm of the method is easy to implement and found to be successful in producing a sufficiently accurate solution with relatively less number of mesh nodes.

Although many error estimation techniques have been developed over the past several years to solve contact problems adaptively, because of boundary non-linearity development, a reliable error estimator needs further investigation. The present study attempts to resolve this problem without having to recompute the entire solution on a new mesh.