The electroencephalogram (EEG) is a record of brain activity. Brain Computer Interface (BCI) technology formed by the EEG signal has become one of the hotspots at present. How to extract the feature signal of EEG is the most basic research of BCI technology. In this paper, A new method of recognizing fatigue, conscious, concentrated state of human brain is proposed by the combination of discrete wavelet transform and the neural network based on EEG signal. First of all, the law signal is preprocessed by the wavelet denoising method because the law EEG signal contains a large number of high frequency noise, which is decomposed into multi-layer high frequency signal and low frequency signal. thus, δ wave, θ wave, α wave, β wave are obtained by the wavelet transform. And then, frequency band energy of the different wave is regards as the feature signal of EEG. In the experiment, the feature signal is classified by radial basic function (RBF) and annealed chaotic competitive learning network (ACCLN). RBF and ACCLN networks are trained with 500 sets of sample data and are tested by 100 sets of samples in different mental states. The experimental results show that the average accuracy of RBF network under three conditions are 88.75%, 88.25%, 88.5%, respectively, and the correct rate of ACCLN network is 97%, 98%, 98%, respectively.

The paper presents an error model of a measurement chain containing link performing discrete wavelet transform algorithm which is most often the last stage of measurement signal processing. The goal is to determine the uncertainty budget of the input quantities of the wavelet transform algorithm. The error model takes into account parts of analog, analog-to-digital and digital processing, describing the properties of subsequent fragments of the chain using their transmittance and processing functions. The proposed model enables the description of both deterministic and non-deterministic properties of signal errors. The proposed model was validated using an example measurement chain created for this purpose.

During routine bridge maintenance, edge detection allows the partial condition of the bridge to be viewed. However, many edge detection methods often have unsatisfactory performances when dealing with images with complex backgrounds. Moreover, the processing often involves the manual selection of thresholds, which can result in repeated testing and comparisons. To address these problems in this paper, the wavelet transform modulus maxima method is used to detect the target image, and then the threshold value of the image can be determined automatically according to the OTSU method to remove the pseudo-edges. Thus, the real image edges can be detected. The results show that the information entropy and SSIM of the detection results are the highest when compared with the commonly used Canny and Laplace algorithms, which means that the detection quality is optimal. To more fully illustrate the advantages of the algorithms, images with more complex backgrounds were detected and the processing results of the algorithms in this paper are still optimal. In addition, the automatic selection of thresholds saves the operator’s effort and improves the detection efficiency. Thanks to the combined use of the above two methods, detection quality and efficiency are significantly improved, which has a good application in engineering practice.

Medical image segmentation is a critical step in various healthcare applications, aiding in diagnosis, treatment planning, and disease monitoring. In this study, we investigate the efficacy of a segmentation approach based on the 2D wavelet transform. Leveraging a dataset comprising 10 diverse medical images, we evaluate the performance of our segmentation method using three key metrics: accuracy, precision, and recall. Our findings demonstrate that the proposed approach enhances segmentation accuracy, offering promising results compared to existing methods. By harnessing the multi-resolution feature extraction capabilities of the 2D wavelet transform, our method achieves improved delineation of medical image structures, paving the way for more accurate and efficient healthcare interventions.

In the process of image feature extraction, noise in the image will greatly affect the accuracy of edge detection. In this paper, the image is filtered to remove noise before edge detection by using the algorithm of wavelet transformation. Different wavelet functions are used to decompose image. Based on the experimental results, the best denoising wavelet function is selected. Canny algorithm is used to detect the edge of the denoised image, and the result of edge detection is evaluated according to the Pratt quality factor. It is proved that wavelet transform can improve the edge detection results.

In this paper we define a continuous wavelet transform of a Schwartz tempered distribution $f \in S^{'}(\mathbb R^n)$ with wavelet kernel $\psi \in S(\mathbb R^n)$ and derive the corresponding wavelet inversion formula interpreting convergence in the weak topology of $S^{'}(\mathbb R^n)$. It turns out that the wavelet transform of a constant distribution is zero and our wavelet inversion formula is not true for constant distribution, but it is true for a non-constant distribution which is not equal to the sum of a non-constant distribution with a non-zero constant distribution.

Estimating the remaining useful life (RUL) of components is a crucial task to enhance the reliability, safety, productivity, and to reduce maintenance cost. In general, predicting the RUL of a component includes constructing a health indicator ( ) to infer the current condition of the component, and modelling the degradation process, to estimate the future behavior. Although many signal processing and data-driven based methods were proposed to construct the , most of the existing methods are based on manual feature extraction techniques, and need the prior knowledge of experts, or rely on a large amount of failure data. Therefore, in this study, a new data-driven method based on the convolutional autoencoder (CAE) is presented to construct the . For this purpose, the continuous wavelet transform (CWT) technique is used to convert the raw acquired vibrational signals into a two-dimensional image; then, the CAE model is trained by the healthy operation dataset. Finally, the Mahalanobis Distance (MD) between the healthy and failure stages is measured as the . The proposed method is tested on a benchmark bearing dataset and compared with several other traditional construction models. Experimental results indicate that the constructed exhibits a monotonically increasing degradation trend and has a good performance to detect incipient faults.

Diabetic retinopathy (DR) is the primary factor leading to vision impairment and blindness in diabetic people. Uncontrolled diabetes can damage the retinal blood vessels. Initial detection and prompt medical intervention are vital in preventing progressive vision impairment. Today's growing medical field poses more significant workload and diagnostic demands on medical professionals. In the proposed study, a convolutional neural network (CNN) is employed to detect the stages of DR. This research is crucial for studying DR because of its innovative methodology incorporating two different public datasets. This strategy enhances the model's capacity to generalize unseen DR images, as each dataset encompasses unique demographics and clinical circumstances. The network can learn and capture complicated hierarchical image features with asymmetric weights. Each image undergoes preprocessing using contrast-limited adaptive histogram equalization (CLAHE) and the discrete wavelet transform (DWT). The model is trained and validated using the combined datasets of Dataset for Diabetic Retinopathy (DDR) and the Asia Pacific Tele-Ophthalmology Society (APTOS). The CNN model is tuned with different learning rates and optimizers. The CNN model with Adam optimizer achieved 70% accuracy and an area under curve (AUC) score of 0.82. The recommended study results may reduce diabetes-related vision impairment by early DR severity identification.

This paper presents the methodology to detect and identify the type of fault that occurs in shunt connected static synchronous compensator (STATCOM) transmission line using a combination of Discrete Wavelet Transform (DWT) and Naive Bayes classifier. To study this, the network model is designed using Mat-lab/Simulink. The different faults such as Line to Ground (LG), Line to Line (LL), Double Line to Ground (LLG) and three-phase (LLLG) fault are applied at different zones of system with and without STATCOM considering the effect of varying fault resistance. The three-phase fault current waveforms obtained are decomposed into several levels using daubechies mother wavelet of db4 to extract the features such as standard deviation and Energy values. The extracted features are used to train the classifiers such as Multi-Layer Perceptron Neural Network (MLP), Bayes and Naive Bayes (NB) classifier to classify the type of fault that occurs in the system. The results reveal that the proposed NB classifier outperforms in terms of accuracy rate, misclassification rate, kappa statistics, mean absolute error (MAE), root mean square error (RMSE), relative absolute error (RAE) and root-relative square error (RRSE) than MLP and Bayes classifier.

Lamb wave-based structural health monitoring is widely acknowledged as a reliable 11 method for damage identification, classification, localization and quantification. However, due to 12 the complexity of Lamb wave signals, especially after interacting with structural components and 13 defects, interpreting these waves and extracting useful information about the structure's health is 14 still a major challenge. However, deep learning-based strategy offers a great opportunity to address 15 such challenges as the algorithm can operate directly on raw discrete time-domain signals. Unlike 16 traditional methods, which often require careful feature engineering and preprocessing, deep learn-17 ing can automatically extract relevant features from the raw data. This paper proposes an autoen-18 coder based on a bidirectional long short-term memory network with maximal overlap discrete 19 wavelet transform layer to detect the signal anomaly and determine the location of the damage in 20 the composite structure. This approach has the potential to greatly enhance our ability to detect and 21 locate structural damage in composite structures, thereby increasing safety and efficiency.

This paper presents a method to detect and classify the high impedance fault that occur in the medium voltage distribution network using discrete wavelet transform (DWT) and adaptive neuro-fuzzy inference system (ANFIS). The network is designed using Matlab software and various faults such as high impedance, symmetrical and unsymmetrical fault have been applied to study the effectiveness of the proposed ANFIS classifier method. This is achieved by training the ANFIS classifier using the features (standard deviation values) extracted from the three phase fault current signal by DWT technique for various cases of fault with different values of fault resistance in the system. The success and discrimination rate obtained for identifying and classifying the high impedance fault from the proffered method is 100% whereas the values are 66.7% and 85% respectively for conventional fuzzy based approach. The results indicate that the proposed method is more efficient to identify and discriminate the high impedance fault accurately from other power system faults in the system.

Bearings are widely used in various types of electrical machinery and equipment. As their core components, failures will often cause serious consequences . At present, most methods of parameter adjustment are still manual adjustment of parameters. This adjustment method is susceptible to prior knowledge and easy to fall into the local optimal solution, failing to obtain the global optimal solution and requires a lot of resources.Therefore, this paper proposes a new method of bearing fault diagnosis based on wavelet packet transform and convolutional neural network optimized by simulated annealing algorithm.The experimental results show that the method proposed in this paper has a more accurate effect in feature extraction and fault classification compared with traditional bearing fault diagnosis methods. At the same time, compared with the traditional artificial neural network parameter adjustment, this paper introduces the simulated annealing algorithm to automatically adjust the parameters of the neural network, thereby obtaining an adaptive bearing fault diagnosis method. To verify the effectiveness of the method, the Case Western Reserve University bearing database was used for testing, and the traditional intelligent bearing fault diagnosis method was compared. The results show that the method proposed in this paper has good results in bearing fault diagnosis. Provides a new way of thinking in the field of bearing fault diagnosis in parameter adjustment and fault classification algorithms

The paper delves into the critical issue of damage detection within the guy cable of a truss steel mast, a pivotal component in structural integrity. It introduces a model wherein damage manifests as a localized cross-section reduction in a single element of the cable. Employing Discrete Wavelet Transform (DWT), a pioneering methodology, the study scrutinizes the behavior of the affected elements through static structural analyses. Signal decomposition via the Mallat pyramid algorithm facilitates comprehensive examination. Static displacements at the connection point between the cable and the truss mast serve as the measured variables. Through systematic investigation, the paper evaluates the impact of damage size and location, external loading force, and cable tension force on the efficacy of the proposed approach. Utilizing data derived from Finite Element Method (FEM) computations for wavelet analysis the authors substantiate the findings with numerical examples, thus offering valuable insights into damage detection strategies for structural health monitoring and engineering applications.

The Doppler band compensated by the keystone transform (KT) is limited. Therefore, it needs to be used in conjunction with the Doppler ambiguity compensation function to correct the range migration (RM) caused by maneuvering targets with Doppler ambiguity. However, the KT implemented by sinc interpolation suffers from significant performance loss at boundaries of compensation Doppler bands. Additionally, in a multi-target scenario, KT implementation methods occupy high complexity when the Doppler range of targets spans over two compensation Doppler bands. To address aforementioned issues, this study presents a variable Doppler starting point keystone transform (VDSPKT) method, where a new form of ambiguity compensation function is constructed, turning the Doppler starting point of the compensation band in KT variable. Firstly, the position of the compensation Doppler band is changed from fixed to adjustable as needed, enhancing the flexibility of KT. Crucially, the connection points of the compensation Doppler bands in sinc interpolation are reset, avoiding the performance loss at their boundaries. Also, the compensation band is adjusted to cover the narrow Doppler frequency range caused by targets, significantly improving the computational efficiency. Finally, the simulation results demonstrate that the proposed approach effectively addresses the performance degradation and high computational complexity of KT in the aforementioned scenarios, resulting in a computational load reduced by approximately 50% compared to traditional methods.

Recognition, decoding and tracking of vortex patterns is of increasing importance in many fields reaching from astronomical observation of distant galaxies to turbulence phenomena in liquids or gases. Currently, coherent light beams with orbital angular momentum (OAM) are of particular interest for optical communication, metrology, micro-machining or particle manipulation. One common task is to identify characteristic spiral patterns in pixelated intensity maps at real-world signal-to-noise ratios. Recently, Fast Fourier Transform (FFT) was applied to the quantitative analysis of spiral interference patterns of OAM beams. Our study considers this approach in more detail. It is demonstrated that specific information can be extracted by combining conformal mapping by polar transform with determining one- or two-dimensional angular frequency spectra either in spatially fixed or scanning mode. Results of proof-of-principle experiments are presented.

This paper is devoted to the study of multi-dimensional integral transform with Fox H-function in the kernel in weighted spaces integrable functions in the domain R+n with positive coordinates. Mapping properties such as the boundedness, the range, the representations of the considered transformation are established.

In Indonesia, types of meat are still identified manually due to increasing prices for beef and buf-falo ahead of Idul Fitri. Traders mix beef with pork to thwart the beef scam. Haar wavelet and GLCM, GLCM with angles of 0°, 45°, 90°, and 135°, as well as matrices using contrast, correlation, energy, homogeneity, and entropy, are used in feature extraction. The following are the results of meat image classification testing using k-NN, Haar wavelet, and GLCM: The k-NN algorithm shows superiority in identifying fresh (99%), frozen (99%), and rotten (96%) meat texture images with the most fantastic accuracy results in every situation. Meanwhile, GLCM routinely provides good results, especially regarding the texture image of fresh meat (183.21) and rotten meat (115.79). However, despite delivering less throughput than k-NN and GLCM, Haar wavelets are still helpful, especially when dealing with fresh meat texture images (89,96).

We present an idea how to use long-wavelength multi-wavelength radio continuum observations of spiral galaxies to isolate magnetic structures which were previously accessible from short-wavelength observations only. The approach is based on the RM-synthesis and 2D continuous wavelet transform. Wavelet analysis helps to recognize a configuration of small-scale structures which are produced by Faraday dispersion. We find that these structures can trace galactic magnetic arms for the case of the galaxy NGC 6946 observed at $\lambda = 17 \div 22$~cm. We support this interpretation by an analysis of a synthetic observation obtained using a realistic model of a galactic magnetic field.

Kim-Kim (Russ. J. Math. Phys. 2017, 24, 241-248) defined the degenerate Laplace transform and investigated some of their certain properties. Motivated by this study, in this paper, we introduce the degenerate Sumudu transform and establish some properties and relations. We derive degenerate Sumudu transforms of power functions, degenerate sine, degenerate cosine, degenerate hyperbolic sine, degenerate hyperbolic cosine, degenerate exponential function, and function derivatives. We also acquire a relationship between degenerate Sumudu transform and degenerate gamma function. Moreover, we investigate a scale preserving theorem for the degenerate Sumudu transform. Furthermore, we show that the degenerate Sumudu transform is the theoretical dual transform to the degenerate Laplace transform.

Saif et al. (J. Math. Comput. Sci. 21 (2020) 127-135) considered modified Laplace transform and developed some of their certain properties and relations. Motivated by this work, in this paper, we define modified Sumudu transform and investigate many properties and relations including modified Sumudu transforms of the power function, sine, cosine, hyperbolic sine, hyperbolic cosine, exponential function, and function derivatives. Moreover, we attain two shifting properties and a scale preserving theorem for the modified Sumudu transform. We give modified inverse Sumudu transform and investigate some relations and examples. Furthermore, we show that the modified Sumudu transform is the theoretical dual transform to the modified Laplace transform.

The twisted Wang transform distribution family, defined as the composition of parameter shifted inverse CDF function with an original CDF function, is found to be most suitable for matching low shape factor distributions, characterizing hard to fit or to simulate reinsurance portfolio losses for some perils from our previous study. Among them, the best form for matching a hard-to-fit empirical loss distribution for a specific peril, is the Exponential Fractional Extra Power 0 Distribution in (0,1) with CDF:.The simplest yet still a good form of this family is the Transformed Hyperbolic Tangent Distribution with CDF:,which has analytical formulas for the moments. The twisted Wang transform distribution family is compared and confirmed to be superior to all other well-known distribution families through extensive numerical optimization practice, distribution forms guesses, and computer-aided exploration experiments.

Sentiment analysis to characterize properties of Bitcoin prices and their forecasting is here developed thanks to the capability of the Fuzzy transform to capture stylized facts and mutual connections between time series having different nature. Six years of daily Bitcoin Prices and Google Trends are analyzed in order to establish new perspectives in the management of their dynamics.

The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In the first part of this two-paper series, we proposed and evaluated the theory of the 2D discrete Fourier Transform (DFT) in polar coordinates. The theory of the actual manipulated quantities was shown, including the standard set of shift, modulation, multiplication, and convolution rules. In this second part of the series, we address the computational aspects of the 2D DFT in polar coordinates. Specifically, we demonstrate how the decomposition of the 2D DFT as a DFT, Discrete Hankel Transform (DHT) and inverse DFT sequence can be exploited for efficient code. We also demonstrate how the proposed 2D DFT can be used to approximate the continuous forward and inverse Fourier transform in polar coordinates in the same manner that the 1D DFT can be used to approximate its continuous counterpart.

In this work, a mixture of Elzaki transform and projected differential transform method is applied to solve a nonlinear wave-like equations with variable coefficients. Nonlinear terms can be easily manipulated by using the projected differential transformation method. The method gives the results show that the proposed method is very efficient, simple and can be applied to other applications.

Marketing is the manner of how to make our sales the best in the market, our prices the most accessible, our clients satisfactory, and thus our brand is the largest distributed. This needs sophisticated and advanced understanding of the total network related. Indeed, marketing data may be seen in different forms such as qualitative and quantitative. However, in the literature, it is easily noticed that large bibliography may be collected about qualitative studies, against few studies on the quantitative point of view. This is a major drawback that makes the marketing science still focusing on the design, although the market is strongly depending on quantities such as money and time. Indeed, marketing data may be a time series such as brand sales per specified periods, brand related-prices over specified periods, market shares, ..., etc. The purpose of the present work is to investigate some marketing models based on time series due to brands. We will precisely study the effect of the time scale on the persistence of brands sales in the market and on the forecasting of such a persistence according to the characteristics of the brand and the related market competition or competitors. Our study is acted on a sample of Saudi brands during the period November 22, 2017 to December 30, 2021.

This paper first introduces the main classification of brain diseases and the main causes of these diseases. It is followed by wavelet analysis, which is a mathematical function or wave-like pattern used to transform data, which can decompose the signal into different wavelet functions, each of which is related to a specific scale or frequency. Wavelet analysis has been applied in many fields such as image processing, data analysis and engineering. In addition, wavelet is also used in the analysis of biological signals. Wavelet analysis breaks down brain signals, such as EEG or fMRI data, into various frequency components at different scales. Wavelet analysis provides time-frequency localization. Pattern recognition can be enhanced by isolating salient features in the data. Wavelet denoising can effectively separate noise from underlying brain signals. Wavelet denoising usually adopts threshold method. Wavelet analysis can enhance pattern recognition by isolating salient features in the data. Researchers can train machine learning models based on these wavelet-derived features to recognize specific patterns associated with different neurological disorders. Wavelet analysis can track these changes by continuously evaluating the frequency content of the neuroimage data over time. Through continuous efforts, wavelet theory and technology have become valuable tools in the field of neuroscience and brain disease research.

By utilizing the Fourier transform, we present a practical method for evaluating a function of a derivative applied to any other arbitrary function of a single complex variable. As an illustration of this approach, we compute the actions of the displacement and squeeze operators on an arbitrary function, as well as the propagation of paraxial fields, Airy and number states, without the need for algebraic quantum operator techniques or the Fresnel integral.

This paper reviews how dynamically adaptive wavelet methods can be designed to simulate atmosphere and ocean dynamics in both flat and spherical geometries. We highlight the special features that these models must have in order to be valid for climate modelling applications. These include exact mass conservation and various mimetic properties that ensure the solutions remain physically realistic, even in the under-resolved conditions typical of climate models. Particular attention is paid to the implementation of complex topography in adaptive models. Using \textsc{wavetrisk} as an example, we explain in detail how to build a semi-realistic global atmosphere or ocean model of interest to the geophysical community. We end with a discussion of the challenges that remain to developing a realistic dynamically adaptive atmosphere or ocean climate models. These include scale-aware subgrid scale parameterizations of physical processes, such as clouds. Although we focus on adaptive wavelet methods, many of the topics we discuss are relevant for adaptive mesh refinement (AMR).

Multiple sclerosis is a chronic, autoimmune disease that mainly affects the central nervous system, including the brain, spinal cord, and optic nerve. This disease can cause clinical symptoms such as cognitive decline, muscle weakness, spasms, and fatigue in patients, and the onset tends to be younger. Current medication can only prevent or alleviate symptoms, so early diagnosis of this disease can increase patients' chances of treatment. Although the use of nuclear magnetic resonance detection can improve the efficiency of early auxiliary diagnosis, it still requires experienced doctors to spend too much time and energy on comprehensive judgment. To reduce the time cost and improve the efficiency of multiple sclerosis diagnosis, this article proposes a detection and recognition algorithm for multiple sclerosis based on wavelet entropy and self-adaptive particle swarm optimization. Firstly, a triple discrete wavelet transform is performed on the brain image of multiple sclerosis, and then 10 wavelet entropies are extracted from the decomposed wavelet subbands, which can reduce the feature dimensions of the image; Then, the algorithm of self-adaptive particle swarm optimization is used to optimize the feedforward neural network, in order to obtain the optimal connection weights and thresholds during the training process. The result of the model is with an average sensitivity of 92.29±1.89, specificity of 92.54±0.67, precision of 92.48±0.59, accuracy of 92.42±0.88, and F1 score of 84.85±1.74, Matthews correlation coefficient of 92.37±0.96, and Fowlkes223 Mallows Index of 92.38±0.96. The experimental results indicate that this algorithm has a very important data support role in detecting multiple sclerosis.

In many application problems, F-transform algorithms are very efficient. In F-transform techniques, we replace the original signal or image with a finite number of weighted averages. The use of weighted average can be naturally explained, e.g., by the fact that this is what we get anyway when we measure the signal. However, most successful applications of F-transform have an additional not-so-easy-to-explain feature: the partition requirement, that the sum of all the related weighting functions is a constant. In this paper, we show that this seemingly difficult-to-explain requirement can also be naturally explained in signal-measuring terms: namely, this requirement can be derived from the natural desire to have all the signal values at different moments of time estimated with the same accuracy.

This algorithm is designed to perform Discrete Fourier Transforms (DFT) to convert temporal data into spectral data. This algorithm obtains the Fourier Transforms by studying the Coefficient of Determination of a series of artificial sinusoidal functions with the temporal data, and normalizing the variance data into a high-resolution spectral representation of the time-domain data with a finite sampling rate. What is especially beneficial about this DFT algorithm is that it can produce spectral data at any user-defined resolution.

In previous studies we used Laurent Schwartz’ theory of distributions to rigorously introduce discretizations and periodizations on tempered distributions. These results are now used in this study to derive a validity statement for four interlinking formulas. They are variants of Poisson’s Summation Formula and connect four commonly defined Fourier transforms to one another, the integral Fourier transform, the Discrete-Time Fourier Transform (DTFT), the Discrete Fourier Transform (DFT) and the Integral Fourier transform for periodic functions—used to analyze Fourier series. We prove that under certain conditions, these four Fourier transforms become particular cases of the Fourier transform in the tempered distributions sense. We first derive four interlinking formulas from four definitions of the Fourier transform pure symbolically. Then, using our previous results, we specify three conditions for the validity of these formulas in the tempered distributions sense.

In view of the problem of cracking easily and partial distortion of images after encryption or decryption, a novel image encryption and decryption algorithm based on Arnod Transform and fractional chaotic is proposed. To begin with, the Arnold transform is used to encrypt. So that the spatial confidence of the original image has been comprehensively disturbed. Secondly, the XOR involving the fractional order chaotic sequence is used to encrypt. The key sequence is dynamically generated to ensure the randomness and difference of key generation. When decryption is required, the first decryption is performed using the key and XOR. Then the second decryption is carried out by using the inverse Arnold transform, and finally the decrypted image is obtained. Experimental results show that the improved algorithm has achieved better performance in encryption and decryption.

This paper presents a novel approach for the recognition of multiple sclerosis (MS) using wavelet entropy and a Particle Swarm Optimization (PSO)-based neural network. MS is a complex neurological disorder with diverse clinical manifestations, often challenging to diagnose accurately. In this study, we leverage wavelet entropy (WE) as a feature extraction method to capture intricate patterns within brain imaging data. These extracted features are then employed to train a neural network model optimized through PSO to enhance classification accuracy. Experimental results on a dataset comprising MS and healthy control subjects demonstrate the effectiveness of our proposed approach, viz., WE-PSONN, which achieves a sensitivity of 91.95±1.15, a specificity of 92.36±0.88, a precision of 92.28±0.88, an accuracy of 92.16±0.90. The combination of advanced signal processing techniques and machine learning optimization holds promise for improving the early diagnosis and management of MS, offering potential benefits to both patients and healthcare providers.

This article examines the wavelet transforms and the machine learning methods in accelerating large eddy simulations of turbulent flows. An overarching challenge of large eddy simulations is to accurately represent the cascade of kinetic energy across the cut-off length scale. Taylor hypothesis suggests that the energy cascade occurs through the process of vortex stretching. However, Richardson hypothesis assumes the self-amplification of the strain field and a hierarchical break down of large eddies lead the energy cascade. The large eddy simulations typically employs the self-amplification of the strain in formulating subgrid models. However, several studies also proposed subgrid models based on vortex stretching. The wavelet-based coherent vortex simulation of turbulence directly accounts for vortex stretching in overall forward scatter of energy, while allowing local backscatter. The wavelet-based large eddy simulation adapts the grid to capture the creation of small-scale eddies, while adopting subgrid models based on the self-amplification of strain. The advancement of artificial intelligence in turbulence modelling is currently evolving around accelerating the numerical simulations of turbulent flow. However, there is a clear connection between the application of wavelet transfroms and neural networks for directly solving the Navier-Stokes equation, indicating some potential benefits of wavelet methods over the neural networks.

The paper investigates new robust code constructions based on bent functions and spline–wavelet transformation. Implementation of bent functions in codes construction increases the probability of error detection in the data channel and cryptographic devices. Meanwhile, use of spline–wavelets theory for constructing the codes gives the possibility to increase system security from the actions of an attacker. Presented constructions combines spline–wavelets functions and bent functions. Developed robust codes, compared to existing ones, have a higher parameter of maximum error masking probability. Illustrated codes are ensuring the security of transmitted information. Some of the granted constructions were implemented on FPGA.

We prove that the Legendre coefficients associated with a function f(x) can be represented as the Fourier coefficients of a suitable Abel-type transform of the function itself. Thus, the computation of N Legendre coefficients can be performed efficiently in O(NlogN) operations by means of a single Fast Fourier Transform of the Abel-type transform of f(x). We also show how the symmetries associated with the Abel-type transform can be exploited to further reduce the computational complexity. The dual problem of calculating the sum of Legendre expansions is also considered. We prove that a Legendre series can be written as the Abel transform of a suitable Fourier series. This fact allows us to state an efficient algorithm for the evaluation of Legendre expansions. Finally, numerical tests are presented to exemplify and confirm the theoretical results.

In this work we present a novel steganography algorithm, based on Fractal Transform domain, combined with the principles of Cryptography. The proposed method uses a private key, which will indicate which segment of the image will be taken and encoded with the Fractal Transform, to then insert the secret bits in the transformed coefficients, thus generating the stego image.

The fractional Hilbert transform, a generalization of the Hilbert transform, has been extensively studied in the literature because of its extensive use in optics, engineering, and signal processing. In the present work, we aimed to expand the fractional Hilbert transform to a space of generalized functions known as Boehmians. We introduce a new fractional convolution operator for the fractional Hilbert transform to prove a convolution theorem similar to the classical Hilbert transform and also to extend the fractional Hilbert transform to Boehmians. We also construct a suitable Boehmian space on which the fractional Hilbert transform exists. Further, we investigate convergence of the fractional Hilbert transform for the class of Boehmians and discuss the continuity of the extended fractional Hilbert transform.

In this paper we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, we analyze the analytical solution for a class of fractional models associated with Logistic model, Von Foerster model and Bertalanffy model is presented graphically for various fractional orders and solution of corresponding classical model is recovered as a particular case.

Breast cancer is the second cause of fatality among all cancers for women. Automatic classification of breast cancer lesions in mammograms is a challenging task due to the irregularity and complexity of the location, size, shape, and texture of these lesions. The intensity dissimilarity has been found between breast cancer tissues and normal tissues, when a multi-spectral anatomical mammographic screening scans have been done. In this work, two approaches have been evaluated to classify the breast tumor lesions. The first one is through Gabor wavelet features and the second one is Statistical features. Subsequently, support vector machine, Multilayer Perceptron and KNN classifiers have been used with computer based method for breast tumor classification.

The paper presents the problem of damage detection in steel girders. Static displacements at the selected point of the structure play the role of measured variables. Structural response signal decomposition is performed according to the Mallat pyramid algorithm, which is used to perform the discrete wavelet transform (DWT). This procedure allows us to quite well determine the location of structural damage. The geometry and the placement of any defective part of the structure may have a random character. It can be assumed that the random processes occurring in the broadly understood structure mechanics are Gaussian in nature. The first four probabilistic moments are estimated using three approaches independent: semi-analytical (SAM), perturbative (SPT), and Monte-Carlo simulations (MCS). The semi-analytical random approach seems to be the most optimal due to the necessary computation time. The incorporation of the mathematical stochastic apparatus into the classical (deterministic) analysis of the statics of the structure makes it possible to estimate the reliability measures of the analyzed girder.

The electroretinography (ERG) is a diagnostic test that measures the electrical activity of the retina in response to a light stimulus. This test has a long history and has been extensively studied among years. Dr. James Dewar recorded the first electroretinogram signal in 1873. Later he described signal analysis using 4 components, namely amplitude, and latency of a-wave and b-wave. Nowadays, the international electrophysiology community has established the standard for electroretinography in 2008. However, from the point of view of signal analysis, the major change did not happen. ERG analysis is still based on the 4 components evaluation. The article describes ERG database including the classification of signals by using advanced analysis of electroretinograms based on wavelet scalogram processing. To implement an extended analysis of the ERG, the parameters extracted from the wavelet scalogram of the signal were obtained using digital image processing and machine learning methods. The results of the study show that the proposed algorithm implements the classification of adult electroretinogram signals by 19% more accurately and pediatric signals by 20% more accurately than the classical algorithm. The promising use of ERG is differential diagnostics, which may also be used in preclinical toxicology and experimental modeling. The problem of developing methods for electrophysiological signals analysis in ophthalmology is associated with the complex morphological structure of electrophysiological signals components, due to the generation of retina cell electrical responses to light stimulus.

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.

Abstract: The two-dimensional Fuzzy Transform was applied in image compression. The quality of the image compressed with this methodis better than that obtained using methods based on fuzzy relation equations and comparable with that of the JPEG method, with better compression execution times. In this paper we propose a variation of the method based on the two-dimensional Fuzzy Transform of image compression, in which the image is first partitioned into blocks and then each block is compressed with the higher compression rate. The advantage of this method consistsinto a greater compression of the image, guaranteeing a high quality of the reconstructed image.The results show that our method is better than the Fuzzy Transform method improving also the quality of the reconstructed image.

The purpose of this work is to study the mechanism of running-in during the friction and to determine the informative parameters characterizing the degree of its completion. During the friction, contact interaction of rough surfaces causes various wave phenomena covering a wide range of frequencies, the subsequent frequency analysis can provide information about the sizes of wave sources and thereby clarify the mechanism of interaction between surface roughness. The using of the wavelet transform for processing of the signals of audible acoustic emission made it possible to determine the beginning and the end of the change in the frequency ranges of the interaction of roughness. The code developed by the authors was used to analyze the acoustic emission signals by using wavelet energy and entropy criteria. The mother wavelet was chosen by carefully evaluating the effectiveness of 54 preliminary candidates for the mother wavelet from 7 wavelet families, ac-cording to three criteria: 1) maximum wavelet energy; 2) Shannon entropy minimum; 3) maximum energy-to-Shannon entropy ratio.

Advances in machine learning (ML) and artificial intelligence (AI) are transforming the way we treat patients in ways not even imagined a few years ago. Cancer research is at the forefront of this movement. Infertility, though not a life-threatening condition, affects around 15% of couples trying for a pregnancy. Increasing availability of large datasets from various sources creates an opportunity to introduce ML and AI into infertility prevention and treatment. At present in the field of assisted reproduction, very little is done in order to prevent infertility from arising, with the main focus put on treatment when often advanced maternal age and low ovarian reserve make it very difficult to conceive. A shift from this disease-centric model to a health centric model in infertility is already taking place with more emphasis on the patient as an active participator in the process. Poor quality and incomplete data as well as biological variability remain the main limitations in the widespread and reliable implementation of AI in the field of reproductive medicine. That said, one of the areas where this technology managed to find a foothold is identification of developmentally competent embryos. More work is required however to learn about ways to improve natural conception, the detection and diagnosis of infertility, and improve assisted reproduction treatments (ART) and ultimately, develop clinically useful algorithms able to adjust treatment regimens in order to assure a successful outcome of either fertility preservation or infertility treatment. Progress in genomics, digital technologies and advances in integrative biology has had a tremendousimpact on research and clinical medicine. With the rise of ‘big data’, artificial intelligence, and the advances in molecular profiling, there is an enormous potential to transform not only scientific research progress, but also clinical decision making towards predictive, preventive, and personalized medicine. In the field of reproductive health, there is now an exciting opportunity to leverage these technologies and develop more sophisticated approaches to diagnose and treat infertility disorders. In this review, we present a comprehensive analysis and interpretation of different innovation forces that are driving the emergence of a system approach to the infertility sector. Here we discuss recent influential work and explore the limitations of the use of Machine Learning models in this rapidly developing area.

We have presented a controllable and human-readable polynomial neural network (CR-PNN) that is the first human-readable neural network. One can imagine its influence on system identification. Subsequently, we developed a relation spectrum in a medical application, which is likely to stand alongside the Fourier spectrum. However, the system analysis methodology is incomplete in contrast to signal processing methodology. Here, we presented the system filters for the first time. In this paper, we used the simulation system to verify the availability of the system analysis methodology. The system analysis methodology showed great properties in system identification and filter. The contribution of this paper is the system analysis methodology: transform method (CR-PNN), relation spectrum, and system filter design.

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

We will show $L^{2}$ boundedness of Discrete Double Hilbert Transform along polynomials satisfying some conditions. Double Hilbert exponential sum along polynomials:$\mu(\xi)$ is Fourier multiplier of discrete double Hilbert transform along polynomials. In chapter 1, we define the reverse Newton diagram. In chapter 2, We make approximation formula for the multiplier of one valuable discrete Hilbert transform by study circle method. In chapter 3, We obtain result that $\mu(\xi)$ is bounded by constants if $|D|\geq2$ or all $(m,n)$ are not on one line passing through the origin. We study property of $1/(qt^{n})$ and use circle method (Propsotion 2.1) to calculate sums. We also envision combinatoric thinking about $\mathbb{N}^{2}$ lattice points in j-k plane for some estimates. Finally, we use geometric property of some inequalities about $(m,n)\in\Lambda$ to prove Theorem 3.3. In chapter 4, We obtain the fact that $\mu(\xi)$ is bounded by sums which are related to $\log_{2}({\xi_{1}-a_{1}\slash {q}})$ and $\log_{2}({\xi_{2}-a_{2}\slash {q}})$ and the boundedness of double Hilbert exponential sum for even polynomials with torsion without conditions in Theorem 3.3. We also use $\mathbb{N}^{2}$ lattice points in j-k plane and Proposition 2.1 which are shown in chapter 2 and some estimates to show that Fourier multiplier of discrete double Hilbert transform is bounded by terms about $\log$ and integral this with torsion is bounded by constants.

In this paper, a technique of image watermarking using multiple images as watermarks is presented. The technique is based on transform domain functions including discrete wavelet transform (DWT), discrete cosine transform (DCT) and singular value decomposition (SVD) with an image as the host signal i.e. the watermarks will be used as proofs of the authenticity of the host image. The technique is executed by performing multilevel DWT followed by applying DCT and SVD to both the host and watermark. Multiple watermarks are used for the insurance of better security level. The scheme is immune to common image processing operations & some attacks and exhibits PSNR of 108.3781dB, normalized cross correlation (NCC) over 0.99 and normalized correlation (NC) over 0.99.

High Efficiency Video Coding (HEVC) uses an 8-point filter and a 7-point filter, which are based on the discrete cosine transform (DCT), for the 1/2-pixel and 1/4-pixel interpolations, respectively. In this paper, discrete sine transform (DST)-based interpolation filters (IF) are proposed. The first proposed DST-based IFs (DST-IFs) use 8-point and 7-point filters for the 1/2-pixel and 1/4-pixel interpolations, respectively. The final proposed DST-IFs use 12-point and 11-point filters for the 1/2-pixel and 1/4-pixel interpolations, respectively. These DST-IF methods are proposed to improve the motion-compensated prediction in HEVC. The 8-point and 7-point DST-IF methods showed average BD-rate reductions of 0.7% and 0.3% in the random access (RA) and low delay B (LDB) configurations, respectively. The 12-point and 11-point DST-IF methods showed average BD-rate reductions of 1.4% and 1.2% in the RA and LDB configurations for the Luma component, respectively.

Analysis of non-stationary and nonlinear sound signals obtained from dynamical processes is one of the greatest challenges in signal processing. Turning machine operation is a highly dynamic process persuaded by many events such as dynamical responses, chip formations and operational conditions of machining. Traditional and widely used fast Fourier transformation and spectrogram is not suitable for processing sound signals acquired from dynamical systems as its result have significant deficiencies because of stationary assumptions and having priori basis. The relatively new technique, Discrete Wavelet Transform, which uses Wavelet decomposition and the recently developed technique, Hilbert Huang Transform (HHT) which uses Empirical Mode Decomposition have notably better properties in the analysis of nonlinear and non-stationary sound signals. This paper presents a comparative study on the decomposition of multicomponent sound signals using Empirical Mode Decomposition and Wavelet Decomposition to highlight the suitability found in HHT to analyze tool-emitted sound signals received from turning processes. Apart from the short mathematical and theoretical foundations of the transformations, this paper demonstrates their decomposition strength using an experimental case study of tool flank wear monitoring in turning. It also concludes HHT is more suitable than DWT to analyze tool-emitted sound signals received from turning processes.

A system of wavelet collocation upwind schemes is constructed for solving hyperbolic conserva-tion laws based on a class of interpolation wavelets. The bias magnitude and symmetry factor are defined to depict the asymmetry of the adopted scaling basis function in wavelet theory. Effects of characteristics of the scaling functions on the schemes are explored based on numerical tests and Fourier analysis. The numerical results reveal that the stability of the constructed scheme is af-fected by the smoothness order, N, and the asymmetry of the scaling function. The dissipation analysis suggests that schemes with Neven have negative dissipation coefficients, leading to unstable behaviors. Only scaling functions with Nodd and bias magnitude of 1 can be used to construct stable upwind schemes due to the non-negative dissipation coefficients. Resolution of the wavelet scheme tends to the spectral resolution as the order of accuracy of the scheme in-creases.

The present paper is concerned with the study of the quality of life index. Such an index has become an important index for measuring the well-being of individuals. However, the quality of life index is always a subjective, intangible, and often hard to quantify with precision due to the lack of quantitative models dealing with. The main goal of the present paper is thus to propose a mathematical, quantitative model for the measurement of a quality of life index. The main novelty is firstly the construction of a wavelet dynamic multiscale model to quantify and investigate the effect of time scale on the quality of life index measuring. The proposed procedure is acted empirically on a sample corresponding to Saudi Arabia as a case of study during the period from 2003 to 2020 as part of the 2030-vision plan. Saudi Arabia has implemented the so-called 2030-vision plan where the quality of life improvement is one of the main goals to be attempted. The findings show that wavelets are capable to localize the time-wise behavior of the index contrarily to classical studies which estimate a global view of the index. Moreover, the study shows the link between the quality of life behavior and many other indices.

Despite the increasing popularity of liquid chromatography-mass spectrometry (LC-MS)-based lipidomics, there is a lack of accepted and validated method for lipid extract quality and quantity assessment prior to LC-MS. Fourier-Transform Infrared Spectroscopy (FTIR) has been reported for quantification of pure lipids, however, the sample complexity and purity complex lipid extract quantification in lipidomics experiments could be impact quantification accuracy. Here, we report comprehensive assessment of the sample matrix on the accuracy of lipid quantification using Attenuated Total Reflectance Fourier-Transform Infrared Spectroscopy (ATR-FTIR). Pure lipids are characterized by CH-and C=O-stretching vibrations on FTIR, with quantitative range of 40–3000 ng and a limit of detection of 12 ng. Sample extraction method and local baseline subtraction during FTIR spectral processing significantly impact lipid quantification by CH-stretching. To facilitate sample quality screening, we developed the Lipid Quality (LiQ) score from a spectral library of common contaminants, using a ratio of peak heights between CH-stretching vibrations maxima and the collective vibrations from amide/amine, CH-stretching minima and sugar moieties. We evaluated LiQ score as a rapid sample quality control method by comparing to total LC-MS intensity of targeted lipidomics of 107 human plasma lipid extracts. Exclusion of poor-quality samples based on LiQ score improved the correlation between FTIR and LC-MS quantification. Finally, the uncertainty of absolute quantification by FTIR was estimated using a 795 ng SPLASH LipidoMix standard to be <10%. In summary, this study identified key parameters for accurate FTIR-based quantification of complex lipid mixture, and developed a rapid workflow requiring only 1 µL of MS-ready sample and < 5 minutes for routine lipidomics sample quality and quantity assessment.

This addendum contains clarifications and a sharpening of some of the results on the VIT transform framework developed in [1]. The focus is on the right-coefficient and left- coefficient forms of the transform, the extraction of a first-order term from a left polynomial fraction, and the application to linear time-varying systems.

Objective:The Glioma brain tumor detection and segmentation methods are proposed in this paper using machine learning approaches. Methods:The boundary edge pixels are detected using Kirsch’s edge detectors and then contrast adaptive histogram equalization method is applied on the edge detected pixels. Then, Ridgelet transform is applied on this enhanced brain image in order to obtain the Ridgelet multi resolution coefficients. Further, features are derived from the Ridgelet transformed coefficients and the features are optimized using Principal Component Analysis (PCA) method and these optimized features are classified into Glioma or non-Glioma brain images using Co-Active Adaptive Neuro Fuzzy Expert System (CANFES) classifier.Results:The proposed method with PCA and CANFES classification approach obtains 97.6% of se, 98.56% of sp, 98.73% of Acc, 98.85% of Pr, 98.11% of FPR and 98.185 of FNR, then the proposed Glioma brain tumor detection method using CANFES classification approach only.

In this paper we survey some recent results due to the author concerning various inequalities and approximations for the finite Hilbert transform of a function belonging to several classes of functions, such as: Lipschitzian, monotonic, convex or with the derivative of bounded variation or absolutely continuous. More accurate estimates in the case that the higher order derivatives are absolutely continuous, are also provided. Some quadrature rules with error bounds are derived. They can be used in the numerical integration of the finite Hilbert transform and, due to the explicit form of the error bounds, enable the user to predict a priory the accuracy.

The continuous advancements in healthcare technology have empowered the discovery, diagnosis, and prediction of diseases, revolutionizing the field. Artificial intelligence (AI) is expected to play a pivotal role in achieving the goals of precision medicine, particularly in disease prevention, detection, and personalized treatment. This study aims to determine the optimal combination of the mother wavelet and AI model for the analysis of pediatric electroretinogram (ERG) signals. The dataset, consisting of signals and corresponding diagnoses, undergoes Continuous Wavelet Transform (CWT) using commonly used wavelets to obtain a time-frequency representation. Wavelet images were used for the training of five widely used deep learning models: VGG-11, ResNet-50, DensNet-121, ResNext-50, and Vision Transformer, to evaluate their accuracy in classifying healthy and unhealthy patients. The findings demonstrate that the combination of Ricker Wavelet and Vision Transformer consistently yields the highest median accuracy values for ERG analysis, as evidenced by the upper and lower quartile values. The median balanced accuracy of the obtained combination of the three considered types of ERG signals in the article are 0.83, 0.85, and 0.88. However, other wavelet types also achieved high accuracy levels, indicating the importance of carefully selecting the mother wavelet for accurate classification. The study provides valuable insights into the effectiveness of different combinations of wavelets and models in classifying ERG wavelet scalograms.

Microgrids of varying size and applications are regarded as a key feature of modernizing the power system. The protection of those systems, however, has become a major challenge and a popular research topic for the reason that it involves greater complexity than traditional distribution systems. This paper addresses the issue through a novel approach which utilizes detailed analysis of current and voltage waveforms through windowed fast Fourier and wavelet transforms. The fault detection scheme involves bagged decision trees which use input features extracted from the signal processing stage and selected by correlation analysis. The technique was tested on a microgrid model developed using PSCAD/EMTDS, which is inspired from an operational microgrid in Goldwind Sc. Tech. Co. Ltd, in Beijing, China. The results showed great level of effectiveness to accurately identify faults from other non-fault disturbances, precisely locate the fault and trigger opening of the right circuit breaker/s under different operation modes, fault resistances and other system disturbances.

After proposing a natural metric for the space in which particles spin which implements the principle of maximum frequency, E=hf is generalised and its inverse Fourier transform is calculated. As a necessary result, a metric is found for the space in which quantum particles spin, hence the possibility of explanation of correlation of spacelike-separated particles is opened up.

Ocean surface waves have been utilized as fundamental information in various fields of oceanic research. In this paper, we suggest a simulation and modelling technique for generating an ocean surface wave using an inverse Fast Fourier Transform (iFFT), and we subsequently verify the wave’s accuracy. The conventional method, linear superposition, requires recursive calculation because of the double summation and the time variable; to circumvent this issue, the new algorithm is presented. The Joint North Sea Wave Project (JONSWAP) spectrum is utilized for the ocean surface wave simulation example, and the parameters are the significant wave height (HS) and the zero-crossing wave period (TZ). A coordinate transform for the wavenumber domain was used to apply the inverse FFT algorithm. To verify the accuracy of the simulation result, the relative error between the input condition and the analysis result was calculated. The result for TZ is below 4% relative error, and the maximum relative error for HS is 7%. To avoid the Nyquist frequency for wave-field analysis and simulation, the minimum grid size was calculated by twice applying the maximum wavenumber.

Over the last few decades, advancements in astrophysics have been closely linked to the development of powerful machine-learning models that can accurately classify celestial bodies. At the same time, however, many astronomical datasets are filled with new features collected by increasingly powerful telescopes. These features can cause overfitting, clouding predictive abilities, and dampening the ability of many models to classify images. Therefore, motivation to design more efficient models has skyrocketed—aiming to optimize for lower run times and high accuracies, even with fewer provided features. In our project, we seek to optimize a convolutional neural network model using a technique known as wavelet analysis. This technique allows us to pick the key features of an astronomical image and accentuate niche details, saving time and boosting accuracy. We applied it to the MiraBest Dataset, a dataset compiled from the FIRST sky survey using a virtual telescope. In the end, after training our neural network on the original images and the five filters (approximation, horizontal, vertical, diagonal, and combined), we found that with fewer features and less overfitting, the vertical Daubechies-family wavelet filter outperformed the original runs with the unaltered images by over 10%. Our findings suggest that wavelet analysis can help harvest the most valuable features in images of celestial bodies–leading to enhanced predictions in astronomical applications and perhaps bolstering modern astrophysical theory.

The spectrums of one type of object under different conditions have the same features (up, down, protruding, concave) at the same spectral positions, which can be used as primary parameters to evaluate the difference among remotely sensed pixels. Wavelet-feature correlation ratio Markov clustering algorithm (WFCRMCA) for the remotely sensed data is proposed based on an accurate description of abrupt spectral features and an optimized Markov clustering in the wavelet feather space. The peak points can be captured and identified by applying a wavelet transform to spectral data. The correlation ratio between two samples is a statistical calculation of the matched peak point positions on the wavelet feature within an adjustable spectrum domain or a range of wavelet scales. The evenly sampled data can be used to create class centers, depending on the correlation ratio threshold at each Markov step, accelerating the clustering speed by avoiding the computation of Euclidean distance for traditional clustering algorithms, such as K-means and ISODATA. Markov clustering applies several strategies, such as a simulated annealing method and gradually shrinking the clustering size, to control the clustering convergence. At each clustering tempera-ture, it can obtain the best class centers quickly. The experimental results of the Airborne Visible/ Infrared Imaging Spectrometer (AVIRIS) and Thermal Mapping (TM) data have verified its ac-ceptable clustering accuracy and high convergence velocity.

This paper explores the application of wavelet analysis, a multiscale approach for enhancing visual clarity, in the context of image denoising, which reduces the impact of noisy pixels, caused by various factors such as electronic sensor limitations, low-light conditions, or transmission errors in digital imaging systems. This paper introduces some common noise types like Gaussian noise and processes of image denoising, eliciting the strength of wavelet analysis. As a powerful image denoising technology, wavelet analysis needs five steps to process the image, and the key step is thresholding. There are many kinds of wavelet, and each wavelet has different advantages and functions, which makes it suitable for different applications. Hence, wavelet analysis also makes a contribution in various fields beyond signal processing and data analysis, such as Biomedical Imaging and Geophysics and Seismology, where preserving image quality is essential for accurate analysis and interpretation. In short, this research highlights the promise of wavelet analysis, emphasizing the use of high- quality image data.

The present work concerns with presenting an explicit formula for new shifted wavelet (NSW) functions. Wavelet functions have many applications and advantages in both applied and theoretical fields. They are formulated with different orthogonal polynomials to construct new techniques for treating some problems in sciences, and engineering. A new important differentiation property of NSW in terms of NSW themselves is obtained and proved in this paper. Then it is utilized together with the state parameterization technique to find solution of optimal control problem (OCP) approximately. The suggested method converts the OCP into a quadratic programming problem, which can be easily determined on computer. As a result, the approximate solution closes with the exact solution even with a small number of NSW utilized in estimation. The error bound estimation for the proposed method is also discussed. Some test numerical examples are solved to demonstrate the applicability of the suggested method. For comparison, the exact known solutions against the obtained approximate results are listed in Tables.

Resolving small molecule mixtures by nuclear magnetic resonance (NMR) spectroscopy has been of great interest for a long time for its precision, reproducibility and efficiency. However, spectral analyses for such mixtures are often highly challenging due to overlapping resonance lines and limited chemical shift windows. The existing experimental and theoretical methods to produce shift NMR spectra in dealing with the problem have limited applicability owing to sensitivity issues, inconsistency and / or requirement of prior knowledge. Recently, we have resolved the problem by decoupling multiplet structures in NMR spectra by the wavelet packet transform (WPT) technique. In this work, we developed a scheme for deploying the method in generating highly resolved WPT NMR spectra and predicting the composition of the corresponding molecular mixtures from their 1H NMR spectra in an automated fashion. The four-step spectral analysis scheme consists of calculating WPT spectrum, peak matching with a WPT shift NMR library, followed by two optimization steps in producing the predicted molecular composition of a mixture. The robustness of the method was tested on an augmented dataset of 1000 molecular mixtures, each containing 3 to 7 molecules. The method successfully predicted the constituent molecules with a median true positive rate of 1.0 against the varying compositions, while a median false positive rate of 0.04 was obtained. The approach can be scaled easily for much larger datasets.

The electric power distribution utility is responsible for providing energy to consumers in a continuous and stable way, failures in the electrical power system reduce the reliability indexes of the grid, directly harming its performance. For this reason, there is a need for failure prediction to reestablish power in the shortest possible time. Considering an evaluation of the number of failures over time, this paper proposes to perform a failure prediction during the first year of the pandemic in Brazil (2020) to verify the feasibility of using time series forecasting models for fault prediction. The Long Short-Term Memory (LSTM) model will be evaluated to obtain a forecast result that can be used by the electric power utility to organize the maintenance teams. The Wavelet transform shows to be promising in improving the predictive ability of the LSTM, making the Wavelet LSTM model suitable for the study at hand. The results show that the proposed approach has better results regarding the evaluation of the error in prediction and has robustness when a statistical analysis is performed.

3D object detection is crucial for autonomous driving to understand the driving environment. Since the pooling operation causes information loss in the standard CNN, we have designed a wavelet multiresolution analysis-based 3D object detection network without a pooling operation. Additionally, instead of using a single filter like the standard convolution, we use the lower-frequency and higher-frequency coefficients as a filter. These filters capture more relevant parts than a single filter, enlarging the receptive field. The model comprises a discrete wavelet transform (DWT) and an inverse wavelet transform (IWT) with skip connections to encourage feature reuse for contrasting and expanding layers. The IWT enriches the feature representation by fully recovering the lost details during the downsampling operation. Element-wise summation is used for the skip connections to decrease the computational burden. We train the model for the Haar and Daubechies (Db4) wavelets. The two-level wavelet decomposition result shows that we can build a lightweight model without losing significant performance. The experimental results on the KITTI’s BEV and 3D evaluation benchmark show our model outperforms the Pointpillars base model by up to 14 \% while reducing the number of trainable parameters. Code will be released.

The Haar wavelet decomposition technique is used to detect the planetary magnetosphere boundaries and discontinuities. We use the magnetometer data from the CASSINI and MESSENGER spacecraft to identify the abrupt changes in the magnetic field when the spacecraft crossed the magnetospheric bow shocks and magnetopauses of Saturn and Mercury, respectively. The results confirm that the Haar transform can efficiently identify the planetary magnetosphere boundaries characterized by the abrupt magnetic field changes. It is suggested that this technique can be applied to detect the planetary boundaries as well as the discontinuities such as the shock waves in the interplanetary space.

The fractional reduced differential transform method is a finite iterative method based on infinite fractional expansions. The result obtained is the approximation of the real value. There are few reports on the approximate error and the applicable condition. In this paper, according to the fractional expansions, we study the factors related to the approximate errors. Our research shows that the approximate errors relate not only to fractional order but also to time $t$ and increase rapidly with time $t$. This method can only be applied within a certain time range and the time range is relevant to fractional order and fractional expansions. Then, many obtained achievements may be incorrect if the applicable conditions are not satisfied. Some examples presented in this paper verify our analysis.

The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In this paper, we propose and evaluate the theory of the 2D discrete Fourier Transform (DFT) in polar coordinates. This discrete theory is shown to arise from discretization schemes that have been previously employed with the 1D DFT and the discrete Hankel Transform (DHT). The proposed transform possesses orthogonality properties, which leads to invertibility of the transform. In the first part of this two-part paper, the theory of the actual manipulated quantities is shown, including the standard set of shift, modulation, multiplication, and convolution rules. Parseval and modified Parseval relationships are shown, depending on which choice of kernel is used. Similar to its continuous counterpart, the 2D DFT in polar coordinates is shown to consist of a 1D DFT, DHT and 1D inverse DFT.

Real time condition monitoring and precision health assessment system is a mandatory need for effective maintenance program in industrial sector. Rapid advancement in the information technology and other engineering technologies have invited more proactive attention from research and development in industrial sectors and particularly in condition monitoring of machines and related Industrial processes. In this work, the drill bit condition monitoring techniques have been developed based on the wavelet analysis and artificial neural network (ANN) as automatic drill bit fault detection and classification. An experimental work has been conducted to capture the vibration signals for analysis. In this experiment, the CNC drill machine is used with high carbon steel drill bit and mild steel material as work piece. The cutting condition parameters are kept constant and the wear level is changed. The Data Acquisition system (DAQ) with Lab VIEW software is used to capture the vibration signals for drill bit with different wear conditions. The captured vibrations data are analyzed using continuous wavelet transform (CWT) with Morlet wavelet and Daubechies wavelet as a prime function. In general, the CWT coefficient is used to generate the inputs features to ANN for automatic tool condition classification, with two outputs (0, 1) for healthy and (1, 0) for faulty. The results show the effectiveness of the combed WT and ANN for automatic classification of tool wear conditions with high success rate.

The universal health insurance system in Taiwan was formed with good intentions to help vulnerable groups. However, the possibility of bankrupting the system due to wasted medical resources. In this study, using the medical expenditures of the Taiwanese Government and gross domestic product (GDP) as variables, the wavelet analysis method was used to empirically study the correlations and leading-lagging relationships in quarterly data in the period from 1996 to 2016. In addition, the dependent population of the insured was used as the control variable. This population had no income and had high medical demands. Results: After the dependent population was included as a control variable, there was a period of low-frequency (one to four years short-term) linkage correlation, as well as a period of high-frequency (four to eight years long-term) linkage correlation. In addition, for more than eight years, there was also a high degree of linkage correlation, indicating that the linkage between medical expenditures and GDP occurred over the long term. Moreover, since medical expenditures positively affected GDP, one-way causality was observed. However, after 2008, regardless of whether a long or short term was examined, there was almost no linkage correlation. Before 2008, the medical expenditures of the government were positively correlated with economic growth; i.e., they enhanced economic growth. But, after 2008, this effect had already disappeared. The universal health insurance system has long been denounced as a waste of medical resources, and the waste must be immediately stopped. The government urgently needs to find a new solution.

We study the application of Optimal Control Theory to Ion Cyclotron Resonance. We test the validity and the efficiency of this approach for the robust excitation of an ensemble of ions with a wide range of cyclotron frequencies. Optimal analytical solutions are derived in the case without any pulse constraint. A gradient-based numerical optimization algorithm is proposed to take into account limitation in the control intensity. The efficiency of optimal pulses is investigated as a function of control time, maximum amplitude and range of excited frequencies. A comparison with adiabatic and SWIFT pulses is done. On the basis of recent results in Nuclear Magnetic Resonance, this study highlights the potential usefulness of optimal control in Ion Cyclotron Resonance.

In this paper, the Fourier-based synchrosqueezing transform (FSST) method is introduced into the power system to realize low frequency oscillation identification. Firstly, the modal components of low frequency oscillation signal are separated by FSST, and calculating the instantaneous parameters including magnitude, frequency and phase of every mode component with Hilbert transform. Then , calculating the damping ration of every modal component based on above parameters and derived the formulas. Thus, it realized effective identification of of modal parameters of low frequency oscillation signal. The experimental results of simulated data and 16-generator system demonstrate the validity and correctness of the FSST method. Comparing with the classical Prony method shows that the FSST method is better in the identification accuracy when the low frequency oscillation signal is polluted by noise. Finally, the effectiveness of the FSST in Actual power grid is verified based on the real data from Sichuan power grid.

In this paper, we proposed a high accurate and stable Legendre transform algorithm which can reduce the potential instability for very high order at a very small increase in the computational time. The error analysis of interpolative decomposition for Legendre transform is presented. By employing block partitioning of Legendre-Vandermonde matrix and butterfly algorithm, a new Legendre transform algorithm with computational complexity O(N(logN)^2/loglogN) in theory and less than O(N(logN)^4) in practical application is obtained. Numerical results are provided to demonstrate the efficiency and numerical stability of the new algorithm.

This study rigorously investigates the impact of COVID-19 on the Tunisian stock market volatility. The investigation spans from January 2020 to December 2022, employing a GJR-GARCH model, bias-corrected wavelet analysis, and an ARDL approach. Specific variables related to health measures and government interventions are incorporated. The findings highlight that confirmed and death cases contribute significantly to the escalation in TUNINDEX volatility. Interestingly, certain indices related to government interventions exhibit no substantial impact on volatility, indicating a weak resilience of the Tunisian stock market amidst the challenges posed by COVID-19. However, the application of the bias-corrected wavelet analysis yields more nuanced outcomes in terms of correlations of volatility to the same metrics. Notably, the study recognizes the potential influence of uncertainties linked to the duration of lockdowns on financial market volatility. The positive and long-term impact on volatility of the US Equity Market uncertainty and VIX is evident through the Autoregressive Distributed Lag Model (ARDL), whereas economic policy uncertainty shows no significant impact. This indicates a potential vulnerability of the Tunisian stock market to future shocks, emphasizing the need for government efforts to instill investor confidence. This comprehensive exploration contributes to our understanding of the dynamics between the pandemic’ metrics, government interventions, and financial market stability. Our findings provide valuable insights for implementing risk management strategies amid the COVID‐19 crisis.

This study develops a wavelet maxima-based methodology to extract anomalous signals from microwave brightness temperature (MBT) observations for seismic estimation. MBT, acquired via satellite microwave radiometry, enables subsurface characterization penetrating clouds. Five earthquake categories were defined contingent on locale (oceanic/terrestrial) and ambient traits (soil hydration, vegetal covering). Continuous wavelet transform was applied to preprocess annualized MBT readings preceding and succeeding prototypical events of each grouping, utilizing optimized wavelet functions and orders tailored to individualized contexts. Wavelet maxima graphs visually portraying signal intensity variations facilitated identification of aberrant phenomena, including pre-seismic accrual, co-seismic perturbation, and postsismic remission signatures. Casework found 10GHz horizontal-polarized MBT optimally detected signals for aquatic and predominantly humid/vegetative settings, whereas 36GHz horizontal-polarized performed best for arid, vegetated landmasses. This preliminary investigation establishes an analytical framework, albeit reliant on qualitative appraisals. Quantitative machine learning methods are warranted to statistically define selection standards and augment empirical forecasting leveraging lithospheric stress state inferences from sensitive MBT parametrization.

This study investigates the complex interplay between public sentiment, as captured through news titles and descriptions, and the stock prices of three major tech companies: Microsoft (MSFT), Tesla (TSLA), and Apple (AAPL). Leveraging advanced analytical methods including Pearson correlation, wavelet coherence, and regression analysis, this research probes the degree to which stock price fluctuations can be attributed to the polarity of media sentiment. The methodology combines statistical techniques to assess sentiment's predictive power on stock opening and closing prices, while wavelet coherence analysis unveils the temporal dynamics of these relationships. Results demonstrate a significant correlation between sentiment polarity and stock prices, with description polarity affecting Microsoft's opening prices, title polarity influencing Tesla's opening prices, and a positive impact of title polarity on Apple's closing prices. However, Tesla's stock showed no significant coherence, indicating a potential divergence in how sentiment affects stock behavior across companies. The study highlights the importance of sentiment analysis in forecasting stock market trends, revealing not only direct correlations but also lagged influences on stock prices. Despite its focus on large-cap tech firms, this research provides a foundational understanding of sentiment's financial implications, suggesting further investigation into smaller firms and other market sectors.

To enhance the overall reliability of the power system, engineers have redirected their focus toward health monitoring and early detection of faults in transformers. Among these faults, transformer core defects demand particular attention. While fault simulation using software has traditionally been the preferred approach, these methods suffer from data inaccuracies in real-world conditions. Consequently, conducting actual experimental setups with induced faults is imperative to investigate core issues. This study uses Hilbert Transform (HT) as a signal processing technique to extract crucial data characteristics, thereby enhancing the performance of the classifier model. The research involves analyzing electric current signals from a single-phase 1kVA transformer. A comparative assessment of our proposed model was conducted using raw data and Fast Fourier Transform (FFT), evaluating accuracy, precision, recall, F1-score, and computational time. The results demonstrate a significant improvement in all metrics for the classifier models, particularly the k-nearest neighbor (KNN) algorithm, which exhibited values of 83.89%, 84.39%, 83.89%, 83.79%, and 0.0156 seconds, respectively. Future work aims to extend this analysis under different loading conditions.

The dynamic evolution and variation of electrical loads is now a priority for optimum management and, above all, forecasting. Indeed, these dynamic load variations require computer tools able to implement optimal load forecasting models. Scientific research into automated models for forecasting electrical loads therefore represents a challenge for scientific researchers. Several research studies have therefore been carried out. These include machine learning approaches such as: LSTM (Long Short-Term Memory), Support Vector Machine (SVM) and others. This article proposes a comparison study between a hybrid model based on the wavelet transform coupled with the adaboost method, and LSTM, for forecasting electricity consumption loads. Python 3.10 was used for the studies. The first results obtained consisted in the study of electricity load forecasts over four (04) data sets of the year (January, April, August and December). These results are very satisfactory, showing a good correlation between the real results of the electrical load consumption data, and the results of the implemented model. The electrical load consumption data are collected from a renewable energy production source: photovoltaic solar energy. The model test results (R2) obtained range from 0.919 to 0.958. These results are representative of real data and reflect the model's performance. The second set of results concerns a comparative study between the methods used by Y. Xie et al (CNN, MLP, LSTM-AM and LSTM-AM-MLP), and our approach. The prediction results obtained between the approaches show a prediction gap ranging from 0.15 to 0.78 for RMSE and 0.83 for MAPE. These results show significant differences between the methods. The minimization of errors by our model, therefore, reflects the model's performance in terms of accuracy, which is necessary for the optimal management of consumer electricity load forecasts in order to ensure balance between supply and demand.

In the present paper, we investigate the impact of the timescale factor on the quality of life index behavior on specific time intervals characterized by the presence of socio-economic, political, and/or health severe movements such as pandemics and crises. We essentially aim to show that effectively the quality of life measuring based on a single index in the existing studies may be described more adequately by a variable index due to the social, political, economic, and also healthy environment. The variability discovered is expressed by the existence and the estimation of a multi-index instead of a single one relatively to many factors. Our focus is mainly on the effect of the COVID-19 pandemic on the quality of life. Our model is applied empirically to a sample corresponding to Saudi Arabia as a case of study during the period from January 1990 to December 2021 as the main period affected by the COVID-19 pandemic. The sample is based on social media conversations and texts discussing and describing the satisfaction with the quality of life. The study confirms effectively that the role of the timescale factor is more described when considering a multi-index rather than measurement on the whole time interval.

The Capital Asset Pricing Model is a widely applied model to describe risky markets and to deduce their systematic risk. Its estimation, therefore, remains an important task in Econo-financial studies. Empirically, it focuses on the impact of return interval on the betas. Existing studies somehow turn around the same idea of measuring the value of the beta according to the uniform intervals of time during a fixed period. However, it is noticed easily, and especially in the last decade that many factors such as socio-political, and Econo-environmental ones have led to a perturbation in the timeline of the worldwide development, and especially in countries and regions having political changes. This led us to introduce a new idea of risk estimation taking into account the non-uniform changes in markets by introducing a non-uniform wavelet analysis. We aim to explain the Econo-political situation of Arab spring countries and the effect of the revolutions on the market beta. The main novelty is firstly the construction of a dynamic backward-forward model for missing data, and next the application of random non-uniform wavelets. The proposed procedure will be acted empirically on a sample corresponding to TUNINDEX stock as a representative index of the Tunisian market actively traded over the period January 14, 2016, to January 13, 2021. The chosen 5-years period is important as it constitutes the first 5-years-after the revolution and depends strongly on the Socio-Econo-political stability in the revolutionary countries.

Fokker-Planck PDEs (incl. diffusions) for stable Lévy processes (incl. Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics, image analysis, directional statistics and probability theory. Exact analytic designs and solutions are known in the 2D case, where they have been obtained using Fourier transform on $SE(2)$. Here we extend these approaches to 3D using Fourier transform on the Lie group $SE(3)$ of rigid body motions. More precisely, we define the homogeneous space of 3D positions and orientations $\mathbb{R}^{3}\rtimes S^{2}:=SE(3)/(\{\mathbf{0}\} \times SO(2))$ as the quotient in $SE(3)$. In our construction, two group elements are equivalent if they are equal up to a rotation around the reference axis. On this quotient we design a specific Fourier transform. We apply this Fourier transform to derive new exact solutions to Fokker-Planck PDEs of $\alpha$-stable Lévy processes on $\mathbb{R}^{3}\rtimes S^{2}$. This reduces classical analysis computations and provides an explicit algebraic spectral decomposition of the solutions. We compare the exact probability kernel for $\alpha = 1$ (the diffusion kernel) to the kernel for $\alpha=\frac12$ (the Poisson kernel). We set up SDEs for the Lévy processes on the quotient and derive corresponding Monte-Carlo methods. We verify that the exact probability kernels arise as the limit of the Monte-Carlo approximations.

Background: The electroretinogram is a clinical test used to assess the function of the photoreceptors and retinal circuits of various cells in the eye, with the recorded waveform being the result of the summated response of neural generators across the retina. Methods: The present investigation involved an analysis of the electroretinogram waveform in both the time and time-frequency domain through the utilization of the discrete wavelet transform and continuous wavelet transform techniques. The primary aim of this study was to monitor and evaluate the effects of treatment in a New Zealand rabbit model of endophthalmitis via electroretinogram waveform analysis and to compare these with normal human electroretinograms Results: The wavelet scalograms were analyzed using various mother wavelets, including the Daubechies, Ricker, Wavelet Biorthogonal 3.1 (bior3.1), Morlet, Haar, and Gaussian wavelets. Distinctive variances were identified in the wavelet scalograms between rabbit and human electroretinograms. The wavelet scalograms in the rabbit model of endophthalmitis showed recovery with treatment in parallel with the time -domain features. Conclusions: The study compared Adult, Child, and Rabbit electroretinogram responses using DWT and CWT, finding that Adult signals had higher power than Child signals, and Rabbit signals showed differences in a-wave and b-wave depending on the type of response tested, while Haar Wavelet was found to be superior in visualizing frequency components in electrophysiological signals in following the treatment of endophthalmitis and may give additional outcome measures for the management of retinal disease.

This paper predict and effectively control the temperature distribution of the steady-state and transient states of anisotropic four-layer composite materials online, knowing the density, specific heat, heat conductivity and thickness of the composite materials. Based on the transfer function, a mathematical model was established to study the dynamic characteristics of heat transfer of the composite materials. First of all, the Fourier heat transfer law was used to establish a one-dimensional Fourier heat conduction differential equation for each composite layer, and the Laplace transformation was carried out to obtain the system function. Then the approximate second-order transfer function of the system was obtained by Taylor expansion, and the Laplace inverse transformation was carried out to obtain the transfer function of the whole system in the time domain. Finally, the accuracy of the simplified analytical solutions of the first, second and third order approximate transfer functions was compared with computer simulation. The results showed that the second order approximate transfer functions can describe the dynamic process of heat transfer better than others. The research on the dynamic characteristics of heat transfer in the composite layer and the dynamic model of heat transfer in composite layer proposed in this paper have a reference value for practical engineering application. It can effectively predict the temperature distribution of composite layer material and reduce the cost of experimental measurement of heat transfer performance of materials.

In this study, a design of Morlet wavelet neural networks (MWNNs) is presented to solve the prediction differential model (PDM) using the global approximation capability of genetic algorithm (GA) and local quick interior-point algorithm scheme (IPAS), i.e., MWNN-GAIPAS. The famous PDM is known as a variant of functional differential system that works as an opposite of the historical delay differential models. A fitness function is optimized using the mean square error by applying the GA-IPAS for solving the PDM. Three PDM examples have been presented numerically to check the authenticity of the MWNN-GAIPAS. For the perfection of the designed MWNN-GAIPAS, the comparability of the obtained results and exact results is performed. Moreover, the neuron analysis is performed by taking the 3, 10 and 20 number of neurons. The statistical observations have been performed to authenticate the reliability of the MWNN-GAIPAS for solving the PDM.

Urban rail transit offers advantages like high safety, energy efficiency, and environmental friendliness. With cities rapidly expanding, travelers are increasingly using rail systems, heightening demands for passenger capacity and efficiency while also pressuring these networks. Passenger flow forecasting is an essential part of transportation systems. Short-term passenger flow forecasting for rail transit can estimate future station volumes, providing valuable data to guide operations management and mitigate congestion. This paper investigates short-term forecasting for Suzhou's Shantang Street station. Shantang Street's high commercial presence and distinct weekday versus weekend ridership patterns make it an interesting test case. Wavelet denoising and LSTM modeling were combined to predict short-term flows, comparing the results to standalone LSTM and SVR approaches. This study illustrates that the adopted algorithms exhibit good performance for passenger prediction. The LSTM model with wavelet denoising proved most accurate, demonstrating applicability for short-term rail transit forecasting and practical significance.

The article examines the relationship between household food waste and GDP in various European regions, aiming to determine how economic prosperity influences household food waste levels. Using comparative analysis of secondary and tertiary data, we developed a synthetic indicator (IpFW), to assess the interaction between GDP per capita and household food waste per capita. Despite expectations, higher GDP did not consistently correlate with lower food waste, challenging assumptions about economic prosperity and environmental stewardship. The research underscores the complex interplay between economic factors and food waste management, revealing no significant correlation even at regional levels. It also highlights the potential of e-commerce in enhancing food waste reduction strategies. E-commerce platforms can optimize food supply chains and consumer behavior, contributing to more sustainable consumption patterns. The conclusions call for a reevaluation of policies and suggest that integrating e-commerce could bolster efforts to manage food waste more effectively, aligning with the Sustainable Development Goals.

Bacterial infections and resistance to antibiotic drugs represent the highest challenges to public health. The search for new and promising compounds with anti-bacterial activity is a very urgent matter. In order to promote the development of platforms enabling to the discovery of compounds with anti-bacterial activity, Fourier Transformed Mid-Infrared (FT-MIR) spectroscopy associated with the machine learning algorithms were used to predict the impact of compounds extracted from Cynara cardunculus against Escherichia coli cells. According to the plant tissue (seeds, dry and fresh leaves, and flowers) and the solvents (ethanol, methanol, acetone, ethyl acetate, and water), compounds with different compositions concerning, phenol content, antioxidant, and antimicrobial activity were obtained. Principal component analysis of spectra, allowed to discriminate compounds that inhibit the E. coli growth, according to the conventional assay. The supervised classification models enabled the prediction of the compound's impact on the E. coli growth, with the accuracy for the test data: Partial least squares-discriminant analysis of 94%; Support vector machines of 89%; k-Nearest neighbor of 72%; and a Backpropagation network of 100%. According to the promising results, the integration of FT-MIR spectroscopy with machine learning presents a high potential to promote the discovery of new compounds with antibacterial activity, thereby streamlining the drug exploratory process.

The diagnosis of Cardio-Vascular diseases (CVD) is highly dependent on analysis of ECG signals. ECG analysis can be helpful in estimating the underlying cause and condition of heart in cardiac abnormality. The effectiveness of ECG signal analysis in detection of CVDs is widely accepted by professional healthcare service provider. Many algorithms have been proposed but almost all of them have some kind of limitations, and these limitations largely influence the effectiveness of ECG analysis. The performed research work is dedicated for design of unique self-organizing maps (SOMs) based neural network for classification of arrhythmia according to a particular ECG signal, the generation of SOMs is based on the certain unique signatures of ECG signals and have potential to classify different cardiac conditions. For extraction of unique features from ECG signals, we have proposed to use Fast Discrete Stockwell Transform (FDST). Since the proposed technique is a result of combining two different techniques hence called as hybrid technology. The purpose of using FDST is to identify unique signatures of ECG signals in a more improved manner than existing one, the term improved is used because it has several advantages over existing techniques such as wavelet and Fourier Transform based methods. Results obtained from the implementation of the technique are capable in visualizing the ECG sinus rhythm and arrhythmia conditions in form of unique SOM for each associated arrhythmia condition. This unique SOM based classification makes them ideal for being used as a diagnostic tool. This ability of arrhythmia classification using FDST and SOMs makes the technique unique and useful providing valuable information about patient condition. Using proposed technology a portable diagnosis tool for monitoring of patient at their site may be facilitated later, that will improve the quality of life of the patient by diagnosing cardiac condition.

The deformation monitoring information of concrete dams contains some high-frequency com-ponents, and the high-frequency components are strongly nonlinear, which reduces the accuracy of dam deformation prediction. In order to solve such problems, this paper proposes a concrete dam deformation monitoring model based on empirical mode decomposition (EMD) combined with wavelet threshold noise reduction and sparrow search algorithm (SSA) optimization of long short-term memory network (LSTM). The model uses EMD combined with wavelet threshold to decompose and denoise the measured deformation data. On this basis, the LSTM model based on SSA optimization is used to mine the nonlinear function relationship between the reconstructed monitoring data and various influencing factors. The example analysis shows that the model has good calculation speed, fitting and prediction accuracy and it can effectively mine the date char-acteristics inherent in the measured deformation, and reduce the influence of noise components on the modeling accuracy.

The special affine Fourier transform (SAFT) is a useful and powerful analyzing tool in signal processing, optics and communications. In this paper, we mainly discuss the randomized nonuniform sampling and reconstruction for random signals bandlimited in the SAFT domain. First, we show that the nonuniform sampling is identical to the uniform sampling after a pre-filter in the sense of second order statistic characters. Then, we propose an approximate reconstruction based on sinc interpolation for the nonuniform sampling of random signals bandlimited in the SAFT domain. Finally, we give the mean square error estimate for the proposed approximate recovery approach.

Texture is essential information for image representation, capturing patterns, and structures. Consequently, texture plays a crucial role in the manufacturing industry and has been extensively studied in the fields of computer vision and pattern recognition. However, real-world textures are susceptible to defects, which can degrade the image quality and cause various issues. Therefore, there is a need for accurate and effective methods to detect texture defects. In this study, a simple autoencoder and Fourier transform were employed for texture defect detection. The proposed method combines Fourier transform analysis with the reconstructed template obtained from the simple autoencoder. Fourier transform is a powerful tool for analyzing the frequency domain of images and signals. Moreover, analyzing the frequency domain enables effective defect detection because texture defects often exhibit characteristic changes in specific frequency ranges. The proposed method demonstrates effectiveness and accuracy in detecting texture defects. Experimental results are presented to evaluate its performance and compare it with those of existing approaches.

Estimation of breeding values through Best Linear Unbiased Prediction (BLUP) using pedigree-based kinship and Marker-Assisted Selection (MAS) are the two fundamental breeding methods used before and after the introduction of genetic markers, respectively. The emergence of high-density genome-wide markers has led to the development of two parallel series of approaches inspired by BLUP and MAS, which are collectively referred to as Genomic Selection (GS). The first series of GS methods alters pedigree-based BLUP by replacing pedigree-based kinship with marker-based kinship in a variety of ways, including weighting markers by their effects in genome-wide association study (GWAS), joining both pedigree and marker-based kinship together in a single-step BLUP, and substituting individuals with groups in a compressed BLUP. The second series of GS methods estimates the effects for all genetic markers simultaneously. For the second series methods, the marker effects are summed together regardless of their individual significance. Instead of fitting individuals as random effects like in the BLUP series, the second series fits markers as random effects. Differing assumptions regarding the underlying distribution of these marker effects have resulted in the development of many Bayesian-based GS methods. This review highlights critical concept developments for both of these series and explores ongoing GS developments in machine learning, multiple trait selection, and adaptation for hybrid breeding. Furthermore, considering the increasing use and variety of GS methods in plant breeding programs, this review addresses important concerns for future GS development and application, such as the use of GWAS-assisted GS, the long-term effectiveness of GS methods, and the valid assessment of prediction accuracy.

The differential transformation, an approach based on Taylor's theorem, is proposed as convenient for finding exact or approximate solution to the initial value problem with multiple Caputo fractional derivatives of generally non-commensurate orders. The multi-term differential equation is first transformed into a multi-order system and then into a system of recurrence relations for coefficients of formal fractional power series. The order of the fractional power series is discussed in relation to orders of derivatives appearing in the original equation. Application of the algorithm to an initial value problem results in a reliable and expected outcome.

Sumudu transform of the Dixon elliptic function with non zero modulus a ≠ 0 for arbitrary powers sm^N(x,a) ; N ≥ 1 ; sm^N(x,a)cm(x,a) ; N ≥ 0 and sm^N(x,a)cm²(x,a) ; N ≥ 0 is given by product of Quasi C fractions. Next by assuming denominators of Quasi C fraction to 1 and hence applying Heliermann correspondance relating formal power series (Maclaurin series of Dixon elliptic functions) and regular C fraction, Hankel determinants are calculated and showed by taking a = 0 gives the Hankel determinants of regular C fraction. The derived results were back tracked to the Laplace transform of sm(x,a) ; cm(x,a) and sm(x,a)cm(x,a).

This article deals with the denoising of signals from sensors (current and voltage) in a photovoltaic conversion chain using wavelet theory. The idea is to reduce the noise as much as possible without distorting or losing the original signal information. To see the reliability of this proposed method, a comparative study between our proposed method (WDD) and the classic low-pass filter method was presented. The contribution in this work is the improvement of the DC-DC boost converter via the use of wavelet theory, however, that’s why we set two objectives: the first is to obtain reliable control of the DC-DC boost converter via the proposed WDD and the second to increase the overall system efficiency. The experimental results show a very great improvement in the quality of the signals of the proposed method compared to the classic method of filtering by low-pass filter.