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Disturbance such as COVID-19, pollution or policy variation to the economic and financial system has significant effect in the big data applications. Hence to study the effect of the disturbance on the related time series plays important role in further applying the big data in economic and financial system. Generalized Weierstrass-Mandelbrot Function is presented to study the complexity of the related time series theoretically and simultaneously. The results show that the disturbance indicated as the exponential form can generate multifractal features for the related time series. And the irregularity and long memory are also simulated by this model and described by the R/S method and multifractal analysis. © 2023 IEEE.
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This paper provides a mathematical fractional-order model that accounts for the mindset of patients in the transmission of COVID-19 disease, the continuous inflow of foreigners into the country, immunization of population subjects, and temporary loss of immunity by recovered individuals. The analytic solutions, which are given as series solutions, are derived using the fractional power series method (FPSM) and the residual power series method (RPSM). In comparison, the series solution for the number of susceptible members, using the FPSM, is proportional to the series solution, using the RPSM for the first two terms, with a proportional constant of ψΓnα+1, where ψ is the natural birth rate of the baby into the susceptible population, Γ is the gamma function, n is the nth term of the series, and α is the fractional order as the initial number of susceptible individuals approaches the population size of Ghana. However, the variation in the two series solutions of the number of members who are susceptible to the COVID-19 disease begins at the third term and continues through the remaining terms. This is brought on by the nonlinear function present in the equation for the susceptible subgroup. The similar finding is made in the series solution of the number of exposed individuals. The series solutions for the number of deviant people, the number of nondeviant people, the number of people quarantined, and the number of people recovered using the FPSM are unquestionably almost identical to the series solutions for same subgroups using the RPSM, with the exception that these series solutions have initial conditions of the subgroup of the population size. It is observed that, in this paper, the series solutions of the nonlinear system of fractional partial differential equations (PDEs) provided by the RPSM are more in line with the field data than the series solutions provided by the FPSM.
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In this paper, we propose to quantitatively compare the loss of human lung health under the influence of the illness with COVID-19, based on the fractal-analysis interpretation of the chest-pulmonary CT pictures, in the case of small datasets, which are usually encountered in medical applications. The fractal analysis characteristics, such as fractal dimension and lacunarity measured values, have been utilized as an effective advisor to interpretation of pulmonary CT picture texture.
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In the present article, we investigate the impact of the timescale factor on the quality of life index behaviour 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 evaluation based on a single index as 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 with relatively too many factors. Our focus is mainly on the effect of the COVID-19 pandemic and crises or crashes on the quality of life. It turns out that the first essays of empirical treatments of such a series bring out a fractal/multifractal aspect. This motivates our main idea reposing on the fractal/multifractal structure of the data to construct a quantitative model based on wavelets combined with change-point analysis. Our model is applied empirically on a sample corresponding to Saudi Arabia as a case of study during the period from January 1990 to December 2021. The end of this period is strongly 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. Besides, this multi-index is clearly illustrated by means of the multifractal spectra of the data used. © 2023 John Wiley & Sons Ltd.
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This study examines asymmetric efficiency and connectedness among halal tourism stocks, green stocks, cryptocurrency, gold, and oil using data covering the period from 2018M12–2022M09. Employing asymmetric multifractal detrended cross-correlation analysis, this study finds gold to be the most efficient asset and halal tourism stocks to be more efficient than green stocks. The asymmetric connectedness approach identifies green stocks as net transmitters of return shocks in all market conditions and halal tourism stocks (oil) as net receivers of return shocks in normal and upward (downward) market conditions. The connectedness among the assets increases during major economic events such as COVID-19 and the Russia–Ukraine war. Portfolio analysis suggests that the minimum connectedness portfolio outperforms all the other methods and shows halal tourism and green stocks offer significant hedging effectiveness. Our findings have significant implications for investors and policymakers seeking to diversify portfolios, manage risks, and regulate information in periods of financial turmoil and asymmetric market conditions. © 2023 Elsevier Ltd
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The paper proposes a compact-sized coronavirus-shaped Microstrip Patch Antenna (MPA) for wireless communication. A 15-20 GHz band of frequency is employed to analyze the effect of the shape on antenna's performance and characteristics. A low-cost FR4 dielectric substrate is used in the design and implementation of the coronavirus-shaped antenna, with suitable dimensions. The proposed antenna has six patterns depending upon the band of frequencies, and the same have been analyzed. The results show that the realized gain is better than -15 dB when using frequencies around 17 GHz, and total efficiency is about 70%. CST microwave software is used for designing and analysis.
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An approach based on fractal scaling analysis to characterize the organization of the Covid-19 genome sequences is presented in this work. The method is based on a multivariate version of the fractal rescaled range analysis implemented on a sliding window scheme to detect variations of long-range correlations over the genome sequence domains. As a preliminary step, the nucleotide sequence is mapped in a numerical sequence by following a Voss rule, resulting in a multichannel sequence represented as a binary matrix. Fractal correlations, quantified in terms of the Hurst exponent, depending on the region of the sequence, where the Covid-19 genome sequences are predominantly random, with some patches of weak long-range correlations. The analysis shows that the regions of randomness are more abundant in the Covid-19 sequences than in the primitive SARS sequence, which suggests that the Covid-19 virus possesses a more diverse genomic structure for replication and infection. The analysis constrained to the surface glycoprotein region shows that the Covid-19 sequence is less random as compared to the SARS sequence, which indicates that the Covid-19 virus can undergo more ordered replications of the spike protein. The Omicron variation exhibits an interesting pattern with some randomness similarities with the other SARS and the Covid-19 genome sequences. Overall, the results show that the multivariate rescaled range analysis provides a suitable framework to assess long-term correlations hidden in the internal organization of the Covid-19 genome sequence. © 2023
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Mathematical modeling can be a powerful tool to predict disease spread in large populations as well as to understand different factors which can impact it such as social distancing and vaccinations. This study aimed to describe the spread the coronavirus disease 2019 (COVID-19) pandemic in Saudi Arabia using a simple discrete variant of the Gompertz model. Unlike time-continuous models which are based on differential equations, this model treats time as a discrete variable and is then represented by a first-order difference equation. Using this model, we performed a short-term prediction of the number of cumulative cases of COVID-19 in the country and we show that the results match the confirmed reports. © 2022 Fractals.
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One of the main motivations for our research was to find a connection between the Brownian motion of microorganisms within fractal nature, with the idea of developing an appropriate procedure and method to control the microorganism's motion direction and predict the position of the microorganism in time. In this paper, we have followed the results of the very rear microorganism's motion sub-microstructures in the experimental microstructure analysisFractals already observed and published. All of these data have been good basis to describe the motion trajectory by time interval method and fractals. We successfully defined the diagrams in two and three-dimensions and we were able to establish the control of Brownian chaotic motion as a bridge between chaotic disorders to control disorder. This significant study opens a new possibility for future investigation and the new potential of total control of the microorganism motion. These perspectives and findings provide significant data for getting more information from these bio systems. They can also be applied, based on self-similarities and biomimetics, to particle physical systemMatterFractalss and matter, generally. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
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The first one studies three procedures of inverse Laplace Transforms: A Sinc–Thiele approximation, a Sinc and a Sinc–Gaussian (SG) method. Classical Iterated Function Systems are composed of a set of Banach contractions giving rise to a fractal attractor in a metric space E. In the reference [3], the authors extend this concept in different ways. Additionally, in the last part of the paper, they consider an infinite collection of maps and multivalued mappings wn:E→K(E), where K(E) is the Hausdorff space of compact subsets of E. The authors prove that under certain conditions, these IFSs own an attractor.
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Face recognition (FR) is a technique for recognizing individuals through the use of face photographs. The FR technology is widely applicable in a variety of fields, including security, biometrics, authentication, law enforcement, smart cards, and surveillance. Recent advances in deep learning (DL) models, particularly convolutional neural networks (CNNs), have demonstrated promising results in the field of FR. CNN models that have been pretrained can be utilized to extract characteristics for effective FR. In this regard, this research introduces the GWOECN-FR approach, a unique grey wolf optimization with an enhanced capsule network-based deep transfer learning model for real-time face recognition. The proposed GWOECN-FR approach is primarily concerned with reliably and rapidly recognizing faces in input photos. Additionally, the GWOECN-FR approach is preprocessed in two steps, namely, data augmentation and noise reduction by bilateral filtering (BF). Additionally, for feature vector extraction, an expanded capsule network (ECN) model can be used. Additionally, grey wolf optimization (GWO) combined with a stacked autoencoder (SAE) model is used to identify and classify faces in images. The GWO algorithm is used to optimize the SAE model’s weight and bias settings. The GWOECN-FR technique’s performance is validated using a benchmark dataset, and the results are analyzed in a variety of aspects. The GWOECN-FR approach achieved a TST of 0.03 s on the FEI dataset, whereas the AlexNet-SVM, ResNet-SVM, and AlexNet models achieved TSTs of 0.125 s, 0.0051 s, and 0.0062 s, respectively. The experimental results established that the GWOECN-FR technology outperformed more contemporary approaches.
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This paper applies recursive right-tailed unit root tests to detect bubble activity for Turkish Lira against financially most-traded five currencies (i.e., the US Dollar (USD/TRY), the British pound (GBP/TRY), the Euro (EUR/TRY), the Chinese Yuan (CNY/TRY) and the Russian Ruble (RUB/TRY)) over January 2, 2015 to February 12, 2021. It can be identified from the Supremum Augmented Dickey-Fuller (SADF) and the Generalized Supremum Augmented Dickey-Fuller (GSADF) tests statistics that there is a high degree of evidence of bubble activity which characterizes all five exchange rates both in the full-sample period and in the sub-periods, including the pre-COVID-19 era (January 2, 2015 to November 15, 2019) and the COVID-19 era (November 18, 2019 to February 12, 2021). The empirical results also indicate that positive bubbles are common for each selected exchange rate and the multiple bubbles were intensified during the COVID-19 period, referring that forex markets became relatively more inefficient compared to the pre-COVID-19 period.
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This study evaluates the Brazilian agricultural commodities market and the dollar-real exchange price variation using the multifractal detrended fluctuations analysis methodology. We investigated the period from January 1, 2019 to September 25, 2019, outside the COVID-19 pandemic, and from January 1, 2020 to September 25, 2020, during the COVID-19 pandemic. We verified the fluctuations of commodities and dollar-real exchange prices during the pandemic caused by COVID-19 showed a record price. The results of Hurst exponent and multifractal parameters α0, w, and r indicate that during the COVID-19 pandemic, sugar was the most efficient commodity, while pork the less one. Compared to the identical months in 2019, the dollar-real exchange was the most efficient market, while ethanol was the least efficient. © 2022 World Scientific Publishing Company.
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We investigate the dynamic correlation between the Bitcoin price (BTC) and the U.S. economic policy uncertainty index (USEPU) from the perspective of multifractality. Utilizing the multifractal detrended cross-correlation analysis (MF-DCCA), we confirm a long-range cross-correlation between BTC and USEPU. Moreover, the empirical results of MF-DCCA show that the power-law properties and multifractal characteristics between BTC and USEPU are significant. We further examine the long-range dependency of cross-correlation between BTC and USEPU series via the Hurst exponent test and confirm the durable cross-correlation. Finally, we introduce another multifractal indicator and examine the extent of multifractality among time series. The empirical results indicate that the BTC series, USEPU series, and the cross-correlation of BTC-USEPU present apparent multifractality, where BTC shows the strongest degree of multifractality.
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We propose a mathematical model for the multifractal dynamics of COVID-19 pandemic. Within this model and the finite-difference parametric nonlinear equations of the reduced SIR (Susceptible-Infected-Removed) model we calculate the fractal dimensions of various segments of daily disease incidence in the world and the variations of COVID-19 basic reproduction number based on the COVID-19 World Statistics data. © 2022 SPIE.
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Singular spectrum analysis (SSA) is a method of time series analysis and is used in various fields, including medicine. A tremorogram is a biological signal that allows evaluation of a person’s neuromotor reactions in order to infer the state of the motor parts of the central nervous system (CNS). A tremorogram has a complex structure, and its analysis requires the use of advanced methods of signal processing and intelligent analysis. The paper’s novelty lies in the application of the SSA method to extract diagnostically significant features from tremorograms with subsequent evaluation of the state of the motor parts of the CNS. The article presents the application of a method of singular spectrum decomposition, comparison of known variants of classification, and grouping of principal components for determining the components of the tremorogram corresponding to the trend, periodic components, and noise. After analyzing the results of the SSA of tremorograms, we proposed a new algorithm of grouping based on the analysis of singular values of the trajectory matrix. An example of applying the SSA method to the analysis of tremorograms is shown. Comparison of known clustering methods and the proposed algorithm showed that there is a reasonable correspondence between the proposed algorithm and the traditional methods of classification and pairing in the set of periodic components.
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Since the industrial revolution, the geopolitics of energy has been a driver of global prosperity and security, and determines the survival of life on our planet. This study examines the nonlinear structure and multifractal behavior of the cross-correlation between geopolitical risk and energy markets (West Texas Intermediate (WTI), Brent, natural gas and heating oil), using the multifractal detrended cross-correlation analysis. Furthermore, an in-depth analysis reveals different associations of the indices of overall geopolitical risk, geopolitical acts, and geopolitical threats against the four energy products. Based on daily data ranging from 1 January 1985 to 30 August 2021, the findings confirm the presence of nonlinear dependencies, suggesting that geopolitical risk and energy markets are interlinked. Furthermore, significant multifractal characteristics are found and the degree of multifractality is stronger between the overall geopolitical risk and WTI while the lowest degree of multifractality is with Brent. Overall, for the WTI and heating-oil markets, the influence of geopolitical threats is more pronounced rather than their fulfilment. Contrarily, the Brent and natural gas are more correlated to geopolitical acts. Energy products exhibit heterogeneous persistence levels of cross-correlation with all the indicators of geopolitical risk, being more persistent in the case of small fluctuations compared to large fluctuations.
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The subject matter of this study was the processing of arterial blood oxygen saturation data (SaO2). The aim was to investigate the downsampling procedure of the SaO2 records on a broad range of scales. The object of study was a small data set (20 subjects, about 164 seconds duration, sampling rate 300 Hz) borrowed from the well-known portal of medical databases Physionet. The tasks to be solved are a test of the dataset heterogeneity, downsampling of the SaO2 series and its increments in a broad range of possible, checking the randomness of SaO2 series increments, argumentation in favor of applying the theory of Levy-type processes to the SaO2 increments and proving of their self-similarity, the definition of the geometrical fractal and its Hausdorff dimension. The methods used are the Levy-type processes theory, statistical methods, boxes-covering method for fractal structures, the autocorrelation function, and programming within MAPLE 2020. The authors obtained the following results: the dataset comprises three subsets with different variability;the records and their increments remain scale-invariant if the switching frequencies remain lower than the reduced sample rate;the increments of SaO2 records are a Levy-type and self-similar random process;the fractal is the set of positions of the non-zero increments (switch-overs) from a geometrical viewpoint. Conclusions. The scientific novelty of the results obtained is as follows: 1) the fractal nature and the self-similarity of SaO2 records and their increments were proved for the first time;2) authors found the fractal Hausdorff dimensions for the subsets in the range (0.48… 0.73) in dependence on variability;3) authors found the principal possibility of the SaO2 data sizes essential reducing without losses of vital information. © 2022. Gennady Chuiko, Yevhen Darnapuk. All Rights Reserved.
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In recent decades, AIDS has been one of the main challenges facing the medical community around the world. Due to the large human deaths of this disease, researchers have tried to study the dynamic behaviors of the infectious factor of this disease in the form of mathematical models in addition to clinical trials. In this paper, we study a new mathematical model in which the dynamics of CD4+ T-cells under the effect of HIV-1 infection are investigated in the context of a generalized fractal-fractional structure for the first time. The kernel of these new fractal-fractional operators is of the generalized Mittag-Leffler type. From an analytical point of view, we first derive some results on the existence theory and then the uniqueness criterion. After that, the stability of the given fractal-fractional system is reviewed under four different cases. Next, from a numerical point of view, we obtain two numerical algorithms for approximating the solutions of the system via the Adams-Bashforth method and Newton polynomials method. We simulate our results via these two algorithms and compare both of them. The numerical results reveal some stability and a situation of lacking a visible order in the early days of the disease dynamics when one uses the Newton polynomial.
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The current COVID-19 pandemic mainly affects the upper respiratory tract. People with COVID-19 report a wide range of symptoms, some of which are similar to those of common flu, such as sore throat and rhinorrhea. Additionally, COVID-19 shares many clinical symptoms with severe pneumonia, including fever, fatigue, dry cough, and respiratory distress. Several diagnostic strategies, such as the real-time polymerase chain reaction technique and computed tomography imaging, which are more costly than chest radiography, are employed as diagnostic tools. The purpose of this paper is to describe the role of the d-summable information dimension of X-ray images in differentiating several lesions and lung illnesses better than both fractal and information dimensions. The statistical analysis shows that the d-summable information dimension model better describes the information obtained from the X-ray images. Therefore, it is a more precise measure of complexity than the information and box-counting dimension. The results also show that the X-ray images of COVID-19 pneumonia reveal greater damage than those of tuberculosis, pneumonia, and various lung lesions, where the damage is minor or much focused. Because the d-summable information dimension increases as the image complexity decreases, it could pave the way to formulate a new measure to quantify the lung damage and assist the clinical diagnosis based on the area under the d-summable information model. In addition, the physical meaning of the nu parameter in the d-summable information dimension is given.