Wavelet Families Research Articles

Using chemometrics methods for determination of aripiprazole and quetiapine as antipsychotic drugs in pharmaceutical mixture and biological fluid by spectrophotometry method based on continuous wavelet transform and multivariate calibration

In this study, two multivariate calibration methods, including partial least squares (PLS) and principal component regression (PCR), as well as continuous wavelet transform (CWT) along with spectrophotometry technique were developed for the simultaneous analysis of Aripiprazole (ARI) and Quetiapine (QTP) in the pharmaceutical formulation and biological fluid. The linear range of ARI and QTP were 1-3 and 2-10 μg mL-1, respectively for the proposed methods. The root mean square error (RMSE) of ARI and QTP related to the test set was obtained 0.014, 0.0758 and 0.194, 0.882 for PLS and PCR methods, respectively. Also, the mean recovery of ARI and QTP was 99.95, 100.04% and 97.38, 98.83% for PLS and PCR models, respectively. Among various families of wavelets in CWT technique, the Coiflet (Coif3) and Symlet (Sym2) families were selected to determine the value of ARI and QTP, respectively. In this method, limit of detection (LOD) and limit of quantification (LOQ) values were found 0.0033, 0.0200 and 0.2764, 0.3486 μg mL-1 for ARI and QTP, respectively. Mean recovery values of ARI and QTP in synthetic mixtures for CWT approach were 96.98%, 98.94%, respectively. One-way analysis of variance (ANOVA) test was applied to compare the results of both mentioned chemometrics models and high-performance liquid chromatography (HPLC) as a reference method. No significant difference was observed between these methods.

A neural pathomics framework for classifying colorectal cancer histopathology images based on wavelet multi-scale texture analysis

Colorectal cancer (CRC) constitutes the third most commonly diagnosed cancer in males and the second in females. Precise histopathological classification of CRC tissue pathology is the cornerstone not only for diagnosis but also for patients’ management decision making. An automated system able to accurately classify different CRC tissue regions may increase diagnostic precision and alleviate clinical workload. However, tissue classification is a challenging task due to the variability in morphological and textural characteristics present in histopathology images. In this study, an artificial neural network was trained to classify between eight classes of CRC tissue image patches derived from a public dataset with 5000 CRC histopathology image tiles. A total of 532 multi-level pathomics features examined at different scales were extracted by visual descriptors such as local binary patterns, wavelet transforms and Gabor filters. An exhaustive evaluation involving a variety of wavelet families and parameters was performed in order to shed light on the impact of scale on pathomics based CRC tissue differentiation. Our model achieved a performance accuracy of 95.3% with tenfold cross validation demonstrating superior performance compared to 87.4% reported in recent studies. Furthermore, we experimentally showed that the first and the second levels of the wavelet approximations can be used without compromising classification performance.

Investigating an efficient and accurate protocol for sampling structures from molecular dynamics simulations: a close look by different wavelet families

Molecular dynamics (MD) simulations are widely used to predict the behavior of molecular systems over time. However, one of the significant challenges of MD simulations is how to treat the thousands of configurations obtained from calculations, since the number of the quantum calculations (QM) required for evaluating electronic parameters is too high and, sometimes, computationally impracticable. Thus, an efficient and accurate sampling protocol is essential for combining classical MD and QM calculations. In this article, based on the OWSCA method, 93 wavelet signals were analyzed in order to further refine the method and identify the best wavelet family for [Fe(H2O)6]2+ and [Mn(H2O)6]2+ complexes in solution. Our results point out that the bior1.3 was the best wavelet; values closest to the experimental data were obtained for both studied systems.

Rapid simultaneous spectrophotometric determination of food dyes in soft drink using continuous wavelet transform and multivariate calibration methods

In this study, the spectrophotometric technique along with chemometrics methods have been developed for the simultaneous determination of sunset yellow (SY) and tartrazine (TZ) in mixtures and soft drink without any prior separation or purification. The first method is the continuous wavelet transform (CWT), in which various wavelet families were investigated. Eventually, the Gaussian wavelet family of second-order with a scaling factor of 5 for SY and the Daubechies wavelet families of the second-order with a scaling factor of 64 for TZ were selected. Both dyes showed good linearity, with the coefficient of determination (R2) of 0.996 and 0.9981 for SY and TZ, respectively. The limit of detection (LOD) and limit of quantification (LOQ) values were 0.1794, 0.0003 𝜇gmL−1 and 0.6066, 0.0983 𝜇gmL−1 for SY and TZ, respectively. On the other hand, multivariate calibration methods, including partial least squares (PLS) and principal component regression (PCR) were studied. The PLS recovery range was obtained from 100.06% to 103.06% and 100.86 to 103.49 for SY and TZ, respectively. Also, the mean recovery (%) of the PCR method were 101.41 and 102.90 for SY and TZ, respectively. In addition, values of RMSE related to the PLS and PCR were achieved 0.2578, 0.3023 and 0.2635, 0.5602 for SY and TZ, respectively. High-performance liquid chromatography (HPLC) as a reference method was applied for the soft drink, and the results were compared with the proposed methods using a one-way analysis of variance (ANOVA). There was no significant difference between them.

EEG Based Evaluation of Examination Stress and Test Anxiety Among College Students

BackgroundAdolescence is a crucial chapter in life and the presence of stress, depression, and anxiety at this stage is a great concern. Prolonged stress is one of the risk factors that may induce suicidal thoughts, destructive ideation, abuse of alcohol, and drugs in adulthood. Based on a record from National Crime Records Bureau, In India over 2320 children were committed suicide per year because of failure in examinations. This raised number implies the severity of this issue and its major impact on society. ObjectivesThe main objective of this paper is to analyze the cognitive stress in students during examination period using EEG biomarkers. Methods and ResultsEEG signal was acquired in two different test conditions such as before examination with 12 minutes and after examination with 3 minutes from 14 subjects with eight electrodes located using wireless Enobio device (Neuro electrics) with 10-20 international lead system. The three brain waves such as theta, alpha, beta relative band energies were considered, and EEG band ratios such as heart rate, neural activity, arousal index, vigilance index and cognitive performance attentional resource index extracted between before and after examination condition using db4 wavelet family with 6 level decomposition. The statistical results suggest that after examination the relative sub-band energies α, β, and θ were decreased significantly (p < 0.05) as compared to before examination. Also, the EEG band ratio such as heart rate and vigilance index shows significant (p < 0.05) decrease after the examination as compared to before examination. It was found that there was a significant (p < 0.05) rise in the arousal index, Cognitive performance attentional resource index (CPARI), and neural activity after the examination as compared to before examination. ConclusionThe experimental results found that the memory and concentration were high before examination, which concludes that adolescence group examination stress was high before examination period as compared to after examination. In the case of gender group comparison, theta energy band for male students was found high compared to female students in before examination state such that it concludes that male students were highly stressed (before examination) than female students. Overall, our results suggest that after examination male students with lower heart rate index than female students which implies the male students control their stress levels as compared to females in the same stress situation.

COMPARISON OF WAVELET TRANSFORM FOR IMAGE RECOGNITION SYSTEM USING LEARNING VECTOR QUANTIZATION

Image is a spatial dimension contains information, color, and not time-dependent. Nowadays image is very important for recognition system as source/data. In order to obtain certain information (features), image transformed or extracted. Wavelet is mathematical function that is able to classify the image energy concentrated on a small group of coefficients (approximation), while other coefficient group (detail) contains very small energy which can be eliminated. This study purpose to compare wavelet family include Haar, Daubechies and Coiflet, then applied to the fingerprint recognition system and face recognition system.There are three major steps in this paper, preprocessing that includes resize normalization, histogram equalization and thresholding, feature extraction using three different wavelet family, learning using Learning Vector Quantization (LVQ) and matching using Euclidean Distance. The experimental result show Haar is the best among the others. In Fingerprint recognition system the accuracy is 85% and 90% for face recognition system.Keywords; Daubichies, Haar, Image Recognition, Learning Vector Quantization, Wavelet Comparison

Fractional biorthogonal wavelets in L 2(ℝ)

The fractional Fourier transform, which is a generalization of the Fourier transform, has become the focus of many research papers in recent years because of its applications in electrical engineering and optics. In this paper, we introduce the notion of fractional biorthogonal wavelets on and obtain the necessary and sufficient conditions for the translates of a single function to form the fractional Riesz bases for their closed linear span. We also provide a complete characterization for the fractional biorthogonality of the translates of fractional scaling functions of two fractional MRA's and the associated fractional biorthogonal wavelet families. Moreover, under mild assumptions on the fractional scaling functions and the corresponding fractional wavelets, we show that the fractional wavelets can generate Reisz bases for

Selection of suitable mother wavelet along with vanishing moment for the effective detection of crack in a beam

Presence of crack in a beam causes a slope discontinuity at the crack location in the operational deflection shape (ODS). Detecting the slope discontinuity in ODS can reveal the presence of crack in a beam. Wavelet transform is a powerful technique to detect discontinuity in a signal. Efficient detection of the crack using wavelet transform depends primarily upon the wavelet family and the number of vanishing moments. In the present work, suitable mother wavelet along with optimum number of vanishing moment is obtained for the effective detection of crack in a beam. Crack detectability is defined to quantify the effectiveness of different mother wavelet and vanishing moments. Finite element analysis is used for getting the simulated ODS. Higher resolution measurement of ODS is the requisite for effective wavelet based crack detection. Photographic method is used for obtaining the high resolution measurement of ODS for the experimental verification. The present methodology works well with the experimentally obtained ODS of the cracked beam. It is capable of detecting crack near the end support also.

Applying Wavelet Filters in Wind Forecasting Methods

Wind is a physical phenomenon with uncertainties in several temporal scales, in addition, measured wind time series have noise superimposed on them. These time series are the basis for forecasting methods. This paper studied the application of the wavelet transform to three forecasting methods, namely, stochastic, neural network, and fuzzy, and six wavelet families. Wind speed time series were first filtered to eliminate the high-frequency component using wavelet filters and then the different forecasting methods were applied to the filtered time series. All methods showed important improvements when the wavelet filter was applied. It is important to note that the application of the wavelet technique requires a deep study of the time series in order to select the appropriate family and filter level. The best results were obtained with an optimal filtering level and improper selection may significantly affect the accuracy of the results.

Day‐ahead and intra‐day wind power forecasting based on feedback error correction

The major hindrance in the development of large-scale grid integration of wind energy into the power system is the production of intermittent and variable power. A largescale integration requires a forecasting mechanism to support the power system operators while operating the grids. This study forecasts the day-ahead and intra-day wind power using the wavelet decomposition, followed by the autoregressive integrated moving average. The forecasting has been attempted on two datasets, actual and error wind power. The forecasting using the wavelet decomposition employs the discrete wavelets consisting of 16 wavelets, grouped into 5 families. The optimum length of the past data used for the model formulation has also been examined for the various scenarios. The forecasting results have been compared based on various performance metrics. The results of the forecasted values have been compared with the reference ARIMA model to see the effectiveness of the proposed wavelet-ARIMA model. The results indicate that the feedback mechanism used in the error dataset have improved the forecasting efficiency over the use of actual data in both the day-ahead and intra-day forecasting. Also, it has been observed that some of the wavelet families outperformed the other families in terms of accuracy and speed.

Development of rapid and simple spectrophotometric method for the simultaneous determination of anti-parkinson drugs in combined dosage form using continuous wavelet transform and radial basis function neural network

In this study, simultaneous measurements of levodopa (LD), carbidopa (CD), and entacapone (ENT) as anti-parkinson drugs were investigated in synthetic mixtures and Staparkin tablet by continuous wavelet transform (CWT) and radial basis function neural network (RBF-NN) along with spectrophotometric method. In the CWT method, based on the best zero crossing point and R squared (R2) related to the calibration solutions, the Symlet with second order (Sym2), the Daubechies with second order (Db2), and Gaussian as wavelet families were selected for LD, CD, and ENT, respectively. Limit of detection (LOD) and limit of quantification (LOQ) of standard samples for LD, CD, and ENT were 0.0076, 0.159, 0.1519 and 0.0055, 0.0148, 0.3854 μg mL−1, respectively. Also, the average recovery of synthetic mixtures, containing LD, CD, and ENT was obtained 100.23%, 100.01%, and 99.88%, respectively. In the RBF-NN model, root mean square error (RMSE) of 1.14 × 10−27, 2.94 × 10−14, and 8.675 × 10−15 were found for LD, CD, and ENT, respectively. The comparison of proposefd methods with each other was performed on a commercial tablet sample through analysis of variance (ANOVA) test at 95% confidence level. In addition, the standard addition technique was applied to evaluate the performance of these methods in complex matrix. Due to the fast, simple, inexpensive, accurate, as well as without need separation steps, the proposed method can compete with high-performance liquid chromatography (HPLC).

A family of Mexican hat wavelet transforms associated with an isometry in the heat equation

In this paper, Green's function of the heat equation is used to obtain one of the forms in a family of Mexican hat wavelet transforms. By implementing the theory of reproducing kernels, an isometry in the heat equation is also investigated. Further, a natural inversion is established for the Mexican hat wavelet transform. Several related recent investigations are also considered.

Source Localization of EEG Brainwaves Activities via Mother Wavelets Families for SWT Decomposition.

A Brain-Computer Interface (BCI) is a system used to communicate with an external world through the brain activity. The brain activity is measured by electroencephalography (EEG) signal and then processed by a BCI system. EEG source reconstruction could be a way to improve the accuracy of EEG classification in EEG based brain-computer interface (BCI). The source localization of the human brain activities can be an important resource for the recognition of the cognitive state, medical disorders, and a better understanding of the brain in general. In this study, we have compared 51 mother wavelets taken from 7 different wavelet families, which are applied to a Stationary Wavelet Transform (SWT) decomposition of an EEG signal. This process includes Haar, Symlets, Daubechies, Coiflets, Discrete Meyer, Biorthogonal, and reverse Biorthogonal wavelet families in extracting five different brainwave subbands for source localization. For this process, we used the Independent Component Analysis (ICA) for feature extraction followed by the Boundary Element Model (BEM) and the Equivalent Current Dipole (ECD) for the forward and inverse problem solutions. The evaluation results in investigating the optimal mother wavelet for source localization eventually identified the sym20 mother wavelet as the best choice followed by bior6.8 and coif5.

Performance of Genetic Algorithm and Levenberg Marquardt Method on Multi-Mother Wavelet Neural Network Training for 3D Huge Meshes Deformation: A Comparative Study

We propose, in this paper, a novel technique for large Laplacian boundary deformations using estimated rotations. The introduced method is used in the domain of Region of Interest (ROI) to align features of mesh based on Multi Mother Wavelet Neural Network (MMWNN) structure found in several mother wavelet families. The wavelet network allows the alignment of the characteristic points of the original mesh towards the target mesh. The key component of our correspondence scheme is a deformation energy that penalizes geometric distortion, encourages structure preservation and simultaneously allows mesh topology changes. To ensure the design of wavelet neural network architecture, an optimization algorithm should be applied to estimate and optimize the network parameters. Therefore, we compare our approach of 3d mesh deformation using MMWNN architecture based on genetic algorithm and our approach relying on Levenberg-Marquardt Method. We also discuss the existing comparison metrics for static and deformed triangle meshes employing the two mentioned approaches. Besides, we enumerate their strengths, weaknesses and relative performance.

Chaotic Duck Traveler Optimization (cDTO) Algorithm for Feature Selection in Breast Cancer Dataset Problem

Objective: 1 of every 3 individuals will be determined to have malignancy in the course of their life. Currently, there are more than 3.8 million ladies who have been determined to have breast malignancy in the United States. 2021 is practically around the bend, yet there's still an ideal opportunity to help ladies confronting breast malignancy in 2020. In this paper, chaotic based duck travel optimization (cDTO) meta-heuristic algorithm is introduced to classifying the input images from Mammogram Image Analysis Society (MIAS) database. Methods: Linear Discriminant Analysis is used to extract the mammogram image features. (cDTO-LDA) is an intrinsic algorithm to remove irrelevant features and select the optimal features by using wavelet families Haar (harr), db4 (daubechies), bior4.4 (Biorthogonal), Symlets (SYM8), “Discrete” FIR approximation of Meyer wavelet (dmey) features. Results: These selected features are evaluated by the quality measures such as accuracy, sensitivity, specificity, error rate that are clearly shows the high exactness of cDTO classifier is 98.5%. CSA-LDA classifier has the minimum exactness. Conclusion: Algorithm efficiency is proved by the promising results achieved by the proposed algorithm for selecting the best feature of breast cancer classification.

Fractional nonuniform multiresolution analysis in L2(ℝ)

To provide a significantly richer representation of non‐stationary signals appearing in various disciplines of science and engineering, we introduce a novel fractional nonuniform multiresolution analysis (FrNUMRA) on the spectrum Λ given by , where is an integer and r is an odd integer with such that r and N are relatively prime. The necessary and sufficient condition for the existence of nonuniform wavelets of fractional order is derived and an algorithm is also presented for the construction of fractional NUMRA starting from a fractional low‐pass filter with appropriate conditions. Besides, we provide a complete characterization for the biorthogonality of the translates of the scaling functions of two fractional nonuniform multiresolution analyses and the associated fractional biorthogonal wavelet families.

A Characterization of Orthonormal Multilevel Wavelet Families in Sobolev Space over Local Fields of Positive Characteristic

In this paper, a characterization of orthonormal multilevel wavelet families in Sobolev space over a local fields of positive characteristic (Hs(K)) is established. Finally an example is presented.

The Optimal Selection of Mother Wavelet Function and Decomposition Level for Denoising of DCG Signal.

The aim of this paper is to find the optimal mother wavelet function and wavelet decomposition level when denoising the Doppler cardiogram (DCG), the heart signal obtained by the Doppler radar sensor system. To select the best suited mother wavelet function and wavelet decomposition level, this paper presents the quantitative analysis results. Both the optimal mother wavelet and decomposition level are selected by evaluating signal-to-noise-ratio (SNR) efficiency of the denoised signals obtained by using the wavelet thresholding method. A total of 115 potential functions from six wavelet families were examined for the selection of the optimal mother wavelet function and 10 levels (1 to 10) were evaluated for the choice of the best decomposition level. According to the experimental results, the most efficient selections of the mother wavelet function are “db9” and “sym9” from Daubechies and Symlets families, and the most suitable decomposition level for the used signal is seven. As the evaluation criterion in this study rates the efficiency of the denoising process, it was found that a mother wavelet function longer than 22 is excessive. The experiment also revealed that the decomposition level can be predictable based on the frequency features of the DCG signal. The proposed selection of the mother wavelet function and the decomposition level could reduce noise effectively so as to improve the quality of the DCG signal in information field.

Damage detection in a 3D wind turbine tower by using extensive multilevel 2D wavelet decomposition and heat map, including soil-structure interaction

The wind-turbine tower is the structure’s supporting pole and accounts for 15% of the total cost. Damage to it may cause the structure’s catastrophic failure. Advances have been made to conditional monitoring systems for the blades and mechanical components inside the nacelle, while less attention has been given to the tower’s health-monitoring efforts. Moreover, the interaction between soil and structure may be significant. This article describes and numerically demonstrates the multi-level 2D wavelet decomposition’s extensive analysis to identify a damaged location in a wind-turbine tower with and without soil-structure interaction. The finite-element model based on the NREL 5-MW reference onshore wind turbine is established and verified. This method uses the 3D mode shape to detect the tower’s damaged location. A novel algorithm was introduced to accelerate and facilitate the damage finite element modeling process of wind turbine towers. An application code was provided to determine the correct 3D directions of the turbine tower meshes. In order to perform extensive calculations, a new algorithm named “Automatic Wavelet Analysis Aid” used to the extraction and automation of the whole wavelets families and their wavelets. Additionally, the conversion of the cylindrical coordinate system to the Cartesian coordinate system was used, and the relationship between the detection of damage accuracy for this proposed transformation is presented. Finally, the heat map illustrations of data and envelope curves are used as a roadmap for damage detection.

Searching for extremal spots in Planck lensing maps

A great deal of attention has been given to the so-called Cold Spot in maps of the cosmic microwave background (CMB) temperature.We present a similar analysis, searching for extremal spots in the CMB lensing convergence and lensing potential maps from the Planck 2018 data release.We perform a multi-scale and multi-filter analysis using the first three members of the Mexican-hat wavelet family to search for extremal features of different shapes and sizes. Although an initial analysis appears to show the existence of some extremal spots at scales below about 5, we conclude, after marginalising over all scales and filters, that no significant features are detected in the lensing maps. We conclude that in terms of maxima and minima of various sizes, the lensing data have similar statistical properties to Gaussian simulations.