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The recent Covid-19 pandemic threw the world into a complete chaos
with its rapid and devastating spread. Scientists are still trying
to obtain a better understanding of the patterns of COVID-19 and
trying to get a deeper understanding of mutant strains and their
pathogenicity by performing genomic sequences of more samples.
Fractal-based analysis provides its unique forecasting policy to
reduce the spread of COVID-19, and in general, to any outbreaks.
The book presents fractal and multifractal models of COVID-19 and
reviews the impact of the pandemic including epidemiology, genome
organization, transmission cycle, and control strategies based on
mathematical models towards developing an immune intervention.
Also, it covers non-clinical aspects such as economic development
with graphical illustrations, meeting the needs of onlookers
outside the sector who desire additional information on the
epidemic. The fractal signatures describe the fractal textures in
the patterns of Corona virus. Studies on the epidemiology of
Covid-19 in relation with the fractals and fractal functions serve
to exhibit its irregular chaotic nature. Moreover, the book with
its wide coverage on the Hurst exponent analysis and the fractal
dimension estimation, greatly aids in measuring the epidemiology.
- New advancements of fractal analysis with applications to many
scientific, engineering, and societal issues - Recent changes and
challenges of fractal geometry with the rapid advancement of
technology - Attracted chapters on novel theory and recent
applications of fractals. - Offers recent findings, modelling and
simulations of fractal analysis from eminent institutions across
the world - Analytical innovations of fractal analysis - Edited
collection with a variety of viewpoints
Most books on fractals focus on deterministic fractals as the
impact of incorporating randomness and time is almost absent.
Further, most review fractals without explaining what scaling and
self-similarity means. This book introduces the idea of scaling,
self-similarity, scale-invariance and their role in the dimensional
analysis. For the first time, fractals emphasizing mostly on
stochastic fractal, and multifractals which evolves with time
instead of scale-free self-similarity, are discussed. Moreover, it
looks at power laws and dynamic scaling laws in some detail and
provides an overview of modern statistical tools for calculating
fractal dimension and multifractal spectrum.
Most books on fractals focus on deterministic fractals as the
impact of incorporating randomness and time is almost absent.
Further, most review fractals without explaining what scaling and
self-similarity means. This book introduces the idea of scaling,
self-similarity, scale-invariance and their role in the dimensional
analysis. For the first time, fractals emphasizing mostly on
stochastic fractal, and multifractals which evolves with time
instead of scale-free self-similarity, are discussed. Moreover, it
looks at power laws and dynamic scaling laws in some detail and
provides an overview of modern statistical tools for calculating
fractal dimension and multifractal spectrum.
This book introduces the fractal interpolation functions (FIFs) in
approximation theory to the readers and the concerned researchers
in advanced level. FIFs can be used to precisely reconstruct the
naturally occurring functions when compared with the classical
interpolants. The book focuses on the construction of fractals in
metric space through various iterated function systems. It begins
by providing the Mathematical background behind the fractal
interpolation functions with its graphical representations and then
introduces the fractional integral and fractional derivative on
fractal functions in various scenarios. Further, the existence of
the fractal interpolation function with the countable iterated
function system is demonstrated by taking suitable monotone and
bounded sequences. It also covers the dimension of fractal
functions and investigates the relationship between the fractal
dimension and the fractional order of fractal interpolation
functions. Moreover, this book explores the idea of fractal
interpolation in the reconstruction scheme of illustrative
waveforms and discusses the problems of identification of the
characterizing parameters. In the application section, this
research compendium addresses the signal processing and its
Mathematical methodologies. A wavelet-based denoising method for
the recovery of electroencephalogram (EEG) signals contaminated by
nonstationary noises is presented, and the author investigates the
recognition of healthy, epileptic EEG and cardiac ECG signals using
multifractal measures. This book is intended for professionals in
the field of Mathematics, Physics and Computer Science, helping
them broaden their understanding of fractal functions and
dimensions, while also providing the illustrative experimental
applications for researchers in biomedicine and neuroscience.
This book introduces the fractal interpolation functions (FIFs) in
approximation theory to the readers and the concerned researchers
in advanced level. FIFs can be used to precisely reconstruct the
naturally occurring functions when compared with the classical
interpolants. The book focuses on the construction of fractals in
metric space through various iterated function systems. It begins
by providing the Mathematical background behind the fractal
interpolation functions with its graphical representations and then
introduces the fractional integral and fractional derivative on
fractal functions in various scenarios. Further, the existence of
the fractal interpolation function with the countable iterated
function system is demonstrated by taking suitable monotone and
bounded sequences. It also covers the dimension of fractal
functions and investigates the relationship between the fractal
dimension and the fractional order of fractal interpolation
functions. Moreover, this book explores the idea of fractal
interpolation in the reconstruction scheme of illustrative
waveforms and discusses the problems of identification of the
characterizing parameters. In the application section, this
research compendium addresses the signal processing and its
Mathematical methodologies. A wavelet-based denoising method for
the recovery of electroencephalogram (EEG) signals contaminated by
nonstationary noises is presented, and the author investigates the
recognition of healthy, epileptic EEG and cardiac ECG signals using
multifractal measures. This book is intended for professionals in
the field of Mathematics, Physics and Computer Science, helping
them broaden their understanding of fractal functions and
dimensions, while also providing the illustrative experimental
applications for researchers in biomedicine and neuroscience.
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