Fractal Dimension as a Diagnostic Tool for Cardiac Diseases

Öztürk, Yagmur

doi:10.14741/ijcet/v.9.3.13

Cited by 6 publications

(4 citation statements)

References 9 publications

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“…In fractal geometry, the Minkowski dimension or box-counting dimension is one of the most common used techniques to approximate the fractal dimension of a fractal set in any metric space [70]. However, this method cannot catch the sudden changes happen in the irregular time-series datasets [71]. To explore the complexity of scale-free time-series data, a variety of different nonlinear techniques such as Higuchi algorithm, power spectrum analysis, and Katz algorithm have been highlighted in different areas [72][73][74][75][76][77].…”

Section: Higuchi Fractal Dimension Algorithmmentioning

confidence: 99%

Classification of drought severity in contiguous USA during the past 21 years using fractal geometry

Azizi,

Azizi

2024

EURASIP J. Adv. Signal Process.

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Drought is characterized by a moisture deficit that can adversely impact the environment, economy, and society. In North America, like many regions worldwide, predicting the timing of drought events is challenging. However, our novel study in climate research explores whether the Drought Monitor database exhibits fractal characteristics, represented by a single scaling exponent. This database categorizes drought areas by intensity, ranging from D0 (abnormally dry) to D4 (exceptional drought). Through vibration analysis using power spectral densities (PSD), we investigate the presence of power-law scaling in various statistical moments across different scales within the database. Our multi-fractal analysis estimates the multi-fractal spectrum for each category, and the Higuchi algorithm assesses the fractal complexity, revealing that D4 follows a multi-fractal pattern with a wide range of exponents, while D0 to D3 exhibit a mono-fractal nature with a narrower range of exponents.

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Section: Higuchi Fractal Dimension Algorithmmentioning

confidence: 99%

Classification of drought severity in contiguous USA during the past 21 years using fractal geometry

Azizi,

Azizi

2024

EURASIP J. Adv. Signal Process.

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“…Although, this method can successfully measure the self-similarity of a fractal process, however, it fails when the sudden changes happen in the irregular time series data sets [37]. To solve this problem, a variety of different non-linear methods such as Higuchi algorithm, power spectrum analysis, and Katz algorithm have been developed by different researchers [25,29].…”

Section: Higuchi Fractal Dimension Algorithmmentioning

confidence: 99%

Non-Integer Dimension of Seasonal Land Surface Temperature (LST)

Azizi¹,

Azizi²

2023

Preprint

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During few last years, climate change including global warming which is attributed to human activities and also its long-term adverse effects on the planet’s functions have been identified as the most challenging discussion topics which have arisen many concerns and efforts to find the possible solutions. Since the warmth arising from Earth’s landscapes affects the world’s weather and climate patterns, we decided to study the changes in the Land Surface Temperature (LST) patterns in different seasons through non-linear methods. Here, we particularly want to estimate the non-integer dimension and fractal structure of the land surface temperature. For this study, the (LST) data has been obtained during the daytime by the Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA’s Terra satellite. Depending on what time of the year data has been collected, temperatures change in different ranges. Since equatorial regions remain warm, and Antarctica and Greenland remain cold, and also because altitude affects temperature, we selected Riley County in the U.S. state of Kansas, which does not belong to any of this type locations and we are interested to observe the seasonal changes in temperature in this county. The results of the present study show that the Land Surface Temperature (LST) belongs to the class of fractal process with non-integer dimension.

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“…Although this method can successfully measure the self-similarity of a fractal process, it fails when sudden changes happen in irregular time series datasets [54]. To solve this problem, a variety of different nonlinear methods, such as the Higuchi algorithm, power spectrum analysis, and Katz algorithm have been developed by different researchers [55,56].…”

Section: Higuchi Fractal Dimension Algorithmmentioning

confidence: 99%

Noninteger Dimension of Seasonal Land Surface Temperature (LST)

Azizi

2023

Axioms

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During the few last years, climate change, including global warming, which is attributed to human activities, and its long-term adverse effects on the planet’s functions have been identified as the most challenging discussion topics and have provoked significant concern and effort to find possible solutions. Since the warmth arising from the Earth’s landscapes affects the world’s weather and climate patterns, we decided to study the changes in Land Surface Temperature (LST) patterns in different seasons through nonlinear methods. Here, we particularly wanted to estimate the noninteger dimension and fractal structure of the Land Surface Temperature. For this study, the LST data were obtained during the daytime by a Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA’s Terra satellite. Depending on the time of the year data were collected, temperatures changed in different ranges. Since equatorial regions remain warm, and Antarctica and Greenland remain cold, and also because altitude affects temperature, we selected Riley County in the US state of Kansas, which does not belong to any of these location types, and we observed the seasonal changes in temperature in this county. According to our fractal analysis, the fractal dimension may provide a complexity index to characterize different LST datasets. The multifractal analysis confirmed that the LST data may define a self-organizing system that produces fractal patterns in the structure of data. Thus, the LST data may not only have a wide range of fractal dimensions, but also they are fractal. The results of the present study show that the Land Surface Temperature (LST) belongs to the class of fractal processes with a noninteger dimension. Moreover, self-organized behavior governing the structure of LST data may provide an underlying principle that might be a general outcome of human activities and may shape the Earth’s surface temperature. We explicitly acknowledge the important role of fractal geometry when analyzing and tracing settlement patterns and urbanization dynamics at various scales toward purposeful planning in the development of human settlement patterns.

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Fractal Dimension as a Diagnostic Tool for Cardiac Diseases

Cited by 6 publications

References 9 publications

Classification of drought severity in contiguous USA during the past 21 years using fractal geometry

Classification of drought severity in contiguous USA during the past 21 years using fractal geometry

Non-Integer Dimension of Seasonal Land Surface Temperature (LST)

Noninteger Dimension of Seasonal Land Surface Temperature (LST)

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