In recent years cardiac interbeat interval time series have been investigated by DFA and MF-DFA methods. In this paper instead of investigating cardiac interbeat interval time series, ECG signals are considered, it is shown that the normal and abnormal heart signals have different scaling relations.

Most daily activities need using hands and fingers dexterously. Hand prostheses in disabled people can be controlled using surface Electromyography (sEMG) signals acquired non-invasively by means of surface electrodes connected to superior limbs. After preprocessing 12 electrodes sEMG signals acquired from 10 amputees, different features in time and frequency domains were computed. Considering sEMG as a complex, random, non-stationary, and nonlinear signal a complex nonlinear feature was also extracted by the method of Multifractal detrended fluctuation analysis (MFDFA). Different classification methods including support vector machine (SVM), linear discriminant analysis (LDA), and Multi-Layer Perceptron (MLP) were used to compare their performance in the classification of eight different finger movements. It was observed that the SVM performed better than the two other classifiers in finger movement classification. The best classification accuracy, precision, and recall (sensitivity), by the fusion of the new and traditional features were 98.70%, 98.74%, and 98.67%, respectively. Results showed that addition of the new feature extracted by MFDFA and other traditional features was effective in improving the data acquisitions.

Today, structural health monitoring techniques that can detect damage in early stages have become very important. For these reason, such techniques must be able to detect slight damages. However, a large number of algorithms that have proposed so far for damage detection are unable to identify early-stage damages. One of the approaches that can be employed is Multifractal method. In this paper, a damage detection technique is proposed based on Multifractal detrend fluctuation analysis and blind source separation. In the first stage, the accuracy of three methods of blind source separation is compared and the most efficient method in decomposing structural vibration signals is selected. These methods include blind modal identification, combined method, and sparse coding. Three structural models are employed to investigate efficiency of the procedures which consists of a range of numerical MDOF model with limited degree of freedom to real structures. In the second stage, a damage index is proposed based on the width of Multifractal spectrum. Results show that the aforementioned method is able to identify various damage patterns and can detect slight damages.

the area of this study, which has covered large parts of the western-southwestern of Iran, has a special topographic and climatic variety. As this area is exposed to geomorphological features such as mountain and plain. In this regard, western and southwestern rainfall systems entering the area, show different reactions to these mid-scale phenomenon (Jahanbakhsh et al,2020) that such a process has caused the scale behavior and more complex dynamic structure of the rainfall signal in the area. Therefore, on one hand to cover the whole area and on the other hand in order to have long-term daily rainfall statistics, six synotic stations including Khorramabad, Kermanshah, Sanandaj, Dezful, Ahvaz and Abadan stations were selected that have long-term statistics with 1961-2018 as representatives of this area. Also, in order to identify the scale behavior and the dynamics of the structure of the temporal series of rainfall in the western-southwestern of Iran, the fractal and Multifractal changed fluctuation analysis method was used (DAF2, MF-DFA2). By using fractal-Multifractal analysis of receding fluctuations on daily rainfall signal, it was shown that the rain of all the stations has a scale behavior. In this regard, three different scale periods were identified for records. So that, the fitting of the fluctuation function of DFA2 against different scales show that there are two cross over points that separate three different rainy regimes in the fluctuation function of the stations. These two crossover points are based on a temporal scale of 180 (6 months) and 550 days (approximately 2 years),Therefore, there are three different scale periods including small-scale (less than 6 months), mid-scale (from 6 months to 2 years) and large-scale (more than 2 years) in the rainy temporal series of the stations with different stability and dynamic rainy structure at these three temporal periods. Lovejoy and Mandelbrot, 1985,Matsoukas et al., 2000,Gan et al., 2007,Tan and Gan, (2017) claimed that the existence of cross over points in rainy temporal series, are different mechanisms of raining because temporal scales different. The values of scale exponent in these three periods showed that large-scale rainfalls do not follow a specific spatial pattern and show relatively homogeneous behavior. Although, small-scale raining period has a spatial behavior, in the way that the rain of southwestern stations shows more instability and short-term memory than western stations. Also the results of MF-DFA2 showed that these two cross over points are present in all fluctuations, so that different scale periods are also shown in small to large fluctuations and are not limited to medium period fluctuations. The results of MF-DFA2 showed that the generalized Hurst exponent (hq) has been converged with increasing rainy temporal scale, as the difference between the small fluctuations and large fluctuations, the small-scale temporal series is larger than the large-scale temporal series,Thus, on a small scale, periods with large fluctuations can be clearly distinguished from periods with small fluctuations. Other Multifractal properties, including a decreasing hq with increasing the rank of fluctuation (q), nonlinearity of mass signal in relation to q indicate the Multifractal nature and multiple scale behavior and nonlinear memory of the rainy signal of the studied stations (Adresh et al. 2020,Shimizu et al., 2002, Bunde et al., 2012,Tan and Gan, 2017). On one hand, the comparison of the parameters of the singularity spectrum of the stations shows that all the singularity parameters are similar in the area, but have different intensities. In this regard, the singularity spectrum of all stations in the area is asymmetric and has long left tails. Such a tendency in the singularity spectrum indicates the predominant role of large fluctuations in the Multifractal structure of the rainy signal (Telesca and Lovallo, 2011). Thus, the shape of the singularity spectrum reveals that the rainy temporal series in the area has such a Multifractal structure which is sensitive to local fluctuations with large values (Kalamaras et al., 2017). In this regard, the rainy temporal series in Khorramabad, Kermanshah and Dezful stations were more complex than other temporal series and Abadan and Ahvaz stations showed a very unstable and noisy structure. On the other hand, the extreme rainfall of southwestern stations including Abadan, Ahvaz and Dezful are much more unstable than the western stations and show heavy rainfall. In this regard, although the structure of Sanandaj station rainfall series is highly sensitive to extreme rainfall, but the intensity of its instability rainfall is lower than the limit rainfall of southwestern stations such as Dezful, which are less sensitive to that of Sanandaj. Its scale exponent is equal to 0. 67 with the scale exponent of Khorramabad and Kermanshah stations. In general, such results indicate complexities of temporal series s of rainfall that have very strong local fluctuations.

In this study, we investigated the surface morphology of Au coatings using atomic force microscopy (AFM). we aimed to understand the growth mechanisms and control the nano- and micro-structure of the films to achieve desired morphological properties. The study focused on films formed by the electrodeposition technique and examined the morphology evolution as a function of film thickness. To verify the crystalline structure of the films, X-ray diffraction (XRD) technique was employed. Statistical tests were conducted to confirm that the gold thin film surfaces under investigation exhibited Multifractal properties. It is found that as the film thickness increased, the Multifractality of the films became more pronounced, and the nonuniformity of the height probabilities also increased. Furthermore, it was observed that surfaces with greater roughness displayed larger nonlinearity and wider width of the Multifractal spectrum. The results indicated that the Multifractal spectrum had a right-hook shape, distinguishing between different film thicknesses even in small sizes of hundreds of nanometers. Overall, this study provides important insights into the surface morphology of Au coatings and highlights the significance of controlling growth mechanisms for fabricating flat Au films with desired morphological properties. These findings have implications for various applications in biological, electronic, and optical devices.

Background: Due to the high level of cytogenetic heterogeneity in osteosarcoma, personalized treatment is the promising strategy for the improvement in outcomes. This is currently not possible due to the absence of targeted therapies and reliable predictors for response to induction chemotherapy. Objectives: To investigate the predictive value of computational analysis of osteosarcoma magnetic resonance (MR) images. Patients and Methods: Multifractal analysis was performed on MR images of primary osteosarcoma of long tubular bones prior to OsteoSa induction chemotherapy. A total of 900 images derived from 67 good and poor responder patients were classified and compared to the actual retrospective outcome. Results: Among the six calculated Multifractal features, Dqmax exerted the highest predictive value with the prediction accuracy of 74. 3%, sensitivity of 72. 4% and specificity of 76. 2%. The obtained classification accuracy was validated by a ten V-fold split sample cross validation. The area under the curve (AUC) value for the best-performing Multifractal Dqmax feature was 0. 82 (95% confidence interval, 0. 70-0. 91). Conclusion: These results suggest for the first time that measuring tumor structure by using Multifractal geometry can predict an individual patient response to neoadjuvant cytotoxic therapy. Therefore, it potentially allows precise implementation of alternative treatment options. This predictive approach made use of digital data that is routinely collected but currently still underexploited.

Studying and recognizing the behaviour of securities returns has always been the focus of investors and researchers since the dawn of capital markets. Based on the statistics of the last decade, the stock market has been one of the major centres for making investment and getting high returns. analysis and forecasting the price of financial assets has always been an intriguing topic in both scientific and practical disciplines which created various challenges for financial analysis. Chaos theory and fractal analysis are the latest theories in this regard. The present study has reviewed the information on Tehran Stock Exchange (TSE) companies’ returns between 2014 and 2018 in monthly intervals to measure the Multifractal system, long-term memory (LTM), and weak-form efficiency of the stock return variable. The aim of the study has been addressed by using Hurst’ s rescaled range (R/S) statistic model. Any R/S larger than 0. 5 indicated a correlation between future stock returns and previous returns and that previous data influence the market. Consequently, it is not a random market but has an LTM, a fractal dimension, and is relevant to the Efficient Market Hypothesis (EMH) that confirms these variables.

This paper shows how Multifractal analysis can be used to characterize the spatial distribution of epicenters in the Zagros and Alborz-Kopeh Dagh regions of Iran. The main Multifractal characteristics, Dq, f(aq), tq, aq and a set of Multifractal parameters defined from the shape of the f(aq)-spectrum including the width of f(aq)-spectrum, nonuniformity factor, combined parameter, coefficients of steepness and asymmetry, and vertex of the t(q)-spectrum have been determined. The results show that, in comparison with the Alborz-Kopeh Dagh region the epicentral distribution in the Zagros has a weak Multifractal (i.e. less heterogeneous) structure. Although the f(aq) spectra of both regions were skewed, the directions of skewing were different. The two distinct Multifractal distribution patterns in these regions reflect different underlying seismotectonic processes related to earthquake activity. The diffused seismicity with fewer larger earthquakes relative to smaller ones in the Zagros and relatively low level of discontinuous seismicity with sporadic occurrence of strong destructive events in the Alborz-Kopeh Dagh confirm our findings. The results further suggest that Multifractal analysis provides us with a deep insight into the complex nature of distribution and geometry associated with earthquake-related phenomena that could not be discovered by any other means.