scholarly journals A fractal scaling analysis of the SARS-CoV-2 genome sequence

2022 ◽  
Vol 73 ◽  
pp. 103433
Author(s):  
M. Meraz ◽  
E.J. Vernon-Carter ◽  
E. Rodriguez ◽  
J. Alvarez-Ramirez
Keyword(s):  
Genome Sequence ◽  
Scaling Analysis ◽  
Fractal Scaling

scholarly journals Discriminating brain activity from task-related artifacts in functional MRI: Fractal scaling analysis simulation and application

NeuroImage ◽  
2008 ◽  
Vol 40 (1) ◽  
pp. 197-212 ◽  
Author(s):  
Jae-Min Lee ◽  
Jing Hu ◽  
Jianbo Gao ◽  
Bruce Crosson ◽  
Kyung K. Peck ◽  
...  
Keyword(s):  
Functional Mri ◽  
Brain Activity ◽  
Scaling Analysis ◽  
Fractal Scaling

scholarly journals Fractal scaling analysis of groundwater dynamics in confined aquifers

2017 ◽  
Vol 8 (4) ◽  
pp. 931-949 ◽  
Author(s):  
Tongbi Tu ◽  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Time Series ◽  
Groundwater Level ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Fractal Scaling ◽  
Groundwater Level Fluctuations ◽  
Groundwater Dynamics ◽  
Detrended Fluctuation ◽  
Infinite Moments

Abstract. Groundwater closely interacts with surface water and even climate systems in most hydroclimatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality, and multifractal detrended fluctuation analysis (MF-DFA) and multiscale multifractal analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation, is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes that can model both the long-memory behavior and the Brownian finite-memory behavior.

Optimal fractal-scaling analysis of human EEG dynamic for depth of anesthesia quantification

2007 ◽  
Vol 344 (3-4) ◽  
pp. 212-229 ◽  
Author(s):  
P. Gifani ◽  
H.R. Rabiee ◽  
M.H. Hashemi ◽  
P. Taslimi ◽  
M. Ghanbari
Keyword(s):  
Scaling Analysis ◽  
Depth Of Anesthesia ◽  
Fractal Scaling ◽  
Human Eeg

TARGET DETECTION WITHIN SEA CLUTTER: A COMPARATIVE STUDY BY FRACTAL SCALING ANALYSES

Fractals ◽  
2006 ◽  
Vol 14 (03) ◽  
pp. 187-204 ◽  
Author(s):  
JING HU ◽  
JIANBO GAO ◽  
FRED L. POSNER ◽  
YI ZHENG ◽  
WEN-WEN TUNG
Keyword(s):  
Time Scales ◽  
Fractal Theory ◽  
Weather Conditions ◽  
Radar Signal ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Sea Clutter ◽  
Fractal Scaling ◽  
Robust Detection ◽  
Scaling Analyses

Sea clutter refers to the radar returns from a patch of ocean surface. Accurate modeling of sea clutter and robust detection of low observable targets within sea clutter are important problems in remote sensing and radar signal processing applications. Due to lack of fundamental understanding of the nature of sea clutter, however, no simple and effective methods for detecting targets within sea clutter have been proposed. To help solve this important problem, we apply three types of fractal scaling analyses, fluctuation analysis (FA), detrended fluctuation analysis (DFA), and the wavelet-based fractal scaling analysis to study sea clutter. Our analyses show that sea clutter data exhibit fractal behaviors in the time scale range of about 0.01 seconds to a few seconds. The physical significance of these time scales is discussed. We emphasize that time scales characterizing fractal scaling break are among the most important features for detecting patterns using fractal theory. By systematically studying 392 sea clutter time series measured under various sea and weather conditions, we find very effective methods for detecting targets within sea clutter. Based on the data available to us, the accuracy of these methods is close to 100%.

scholarly journals Fractal Scaling Analysis of Groundwater Dynamics in Confined Aquifers

2017 ◽  
Author(s):  
Tongbi Tu ◽  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Time Series ◽  
Groundwater Level ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Fractal Scaling ◽  
Groundwater Level Fluctuations ◽  
Groundwater Dynamics ◽  
Detrended Fluctuation ◽  
Infinite Moments

Abstract. Groundwater closely interacts with surface water and even climate systems in most hydro-climatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations of confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality; and Multifractal detrended fluctuation analysis (MF-DFA) and Multiscale Multifractal Analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics which may be fitted by the Lévy stable distribution or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes, which can model both the long-memory behavior as well as the Brownian finite-memory behavior.

The origin and loss of fractal scaling in simulated soil aggregates

1997 ◽  
Vol 48 (4) ◽  
pp. 643-650 ◽  
Author(s):  
J. W. CRAWFORD ◽  
S. VERRALL ◽  
I. M. YOUNG
Keyword(s):  
Soil Aggregates ◽  
Fractal Scaling
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