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.

Fractal analysis of time series aims to extract the hidden or complex structures issued from the associated real data, such as scaling laws, non-stationary, dynamics, and so on. In the present work, the air quality index and its components are considered as time series owing fractal structures. To understand their underlying dynamics, wavelet multifractal approach is applied starting with a wavelet multifractal spectrum test to confirm the multifractality of the underlying data. Next, a new model is introduced improving the classical minmax one, provided with a statistical measure for the adequacy of the new model. The theoretical findings are applied to the north west Tabuk region of Saudi Arabia for environmental and climate data related to pollutants and factors involved in the estimation of the air quality index.

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.

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.

In this paper, we propose a new methodology for crack monitoring in concrete structures. This approach is based on a n this paper, we propose a new methodology for monitoring cracks in concrete structures. This approach is based on a multi-resolution analysis of a sample or a specimen of the studied material subjected to several types of solicitation. The image obtained by ultrasonic investigation and processing by a dedicated wavelet will be analyzed according to several scales in order to detect internal cracks and crack initiation. The ultimate goal of this work is to propose an automatic crack type identification scheme based on convolutional neural networks (CNN). In this context, crack propagation can be monitored without access to the concrete surface and the goal is to detect cracks before they are visible on the concrete surface. The key idea allowing such a performance is the combination of two major data analysis tools which are wavelets and Deep Learning. This original procedure allows to reach a high accuracy close to 0.90. In this work, we have also implemented another approach for automatic detection of external cracks by deep learning from publicly available datasets.

The acoustic emission (AE) technique was applied to monitor the pitting corrosion of carbon steel in NaHCO₃ + NaCl solutions. The open circuit potential (OCP) measurement and the corrosion morphology in-situ capturing using optical microscope were conducted during AE monitoring. The corrosion micromorphology was characterized with scanning electron microscope (SEM). The propagation behavior and AE features of natural pitting on carbon steel were investigated. After the performing of signal processing including pre-treatment, shape preserving interpolation and denoising for raw AE waveforms, three types of AE signals can be classified in the correlation diagrams of new waveform parameters. Finally, a 2D pattern recognition method was established to calculate the similarity of different continuous AE graphics, which is quite effective to distinguish the localized corrosion from uniform corrosion.

Discussing quantum theory foundations, von Neumann noted that the measurement process should not be regarded in terms of a temporal evolution. A reason for his claim is insurmountability of the gap between reversible and irreversible processes. The time operator formalism that goes beyond such a gap is adequate framework for elaboration of the measurement problem. It considers signals to be stochastic processes, whether they correspond to variables or distribution densities. Signal processing like that utilizes statistical properties to perform its tasks, which is the definition of statistical signal processing. A hierarchy of the measurement process is indicated by crossing between states and devices, which implies an evolution in the temporal domain. The concept has generalized to an open system by the use of duality in frame theory.

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.

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.

Lithium-ion batteries are key elements in the development of electrical energy storage solutions. However, due to cycling, environmental and operating conditions, battery capacity tends to degrade over time. Capacity fade is a common indicator of battery state of health (SOH) because it is an indication of how capacity has been degraded. However, battery capacity cannot be measured directly, so there is an urgent need to develop methods for estimating battery capacity in real time. By analyzing the historical data of a battery in detail, it is possible to predict the future state of the battery and forecast its remaining useful life. This paper develops a real-time, simple and fast method to estimate the cycle capacity of a battery during the charge cycle using only data from a short period of each charge cycle. This proposal is attractive because it does not require data from the entire charge period, since batteries are rarely charged from zero to full. The proposed method allows simultaneous and accurate real-time prediction of the health and remaining useful life of the battery over its lifetime. The accuracy of the proposed method has been tested using experimental data from several lithium-ion batteries with different cathode chemistries under various test conditions.

Smart grids require flexible data driven forecasting methods. We propose clustering tools for bottom-up short-term load forecasting. We focus on individual consumption data analysis which plays a major role for energy management and electricity load forecasting. The two first sections are dedicated to the industrial context and a review of individual electrical data analysis. We are interested in hierarchical time-series for bottom-up forecasting. The idea is to disaggregate the signal in such a way that the sum of disaggregated forecasts improves the direct prediction. The 3-steps strategy defines numerous super-consumers by curve clustering, builds a hierarchy of partitions and selects the best one minimizing a forecast criterion. Using a nonparametric model to handle forecasting, and wavelets to define various notions of similarity between load curves, this disaggregation strategy applied to French individual consumers leads to a gain of 16\% in forecast accuracy. We then explore the upscaling capacity of this strategy facing massive data and implement proposals using R, the free software environment for statistical computing. The proposed solutions to make the algorithm scalable combines data storage, parallel computing and double clustering step to define the super-consumers.

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).

The first part of the paper was aimed at analyzing the given nonlinear problem by different methods of computation of the Lyapunov exponents (Wolf method [1], Rosenstein method [2], Kantz method [3], method based on the modification of a neural network [4, 5], and the synchronization method [6, 7]) for the classical problems governed by difference and differential equations (Hénon map [8], hyper-chaotic Hénon map [9], logistic map [10], Rössler attractor [11], Lorenz attractor [12]) and with the use of both Fourier spectra and Gauss wavelets [13]. It was shown that a modification of the neural network method [4, 5] makes it possible to compute a spectrum of Lyapunov exponents, and then to detect a transition of the system regular dynamics into chaos, hyper-chaos, hyper hyper-chaos and deep chaos [14-16]. Different algorithms for computation of Lyapunov exponents were validated by comparison with the known dynamical systems spectra of the Lyapunov exponents. The carried out analysis helps comparatively estimate the employed methods in order to choose the most suitable/optimal one to study different kinds of dynamical systems and different classes of problems in both this and the next paper parts.