Abstract: By utilizing the system of the recurrence equations, containing two parameters, the dynamics of two antagonistically interconnected populations is studied. The following areas of the system behavior are detected: the area of the stable solutions, the area of cyclic solutions occurrence, the area of the accidental change of trajectories of solutions, and the area of chaos and fractal phenomena. The new two-dimensional diagram of the dynamics of the solutions change (the fractal cabbage) has been obtained. In the cross-section of this diagram for one of the equations the well-known Feigenbaum tree of doubling has been noted.Keywordsbifurcation, chaos, dynamics of populations, fractals
Abstract: This paper proposes fractal patterns for power quality
(PQ) detection using color relational analysis (CRA) based classifier.
Iterated function system (IFS) uses the non-linear interpolation in the
map and uses similarity maps to construct various fractal patterns of
power quality disturbances, including harmonics, voltage sag, voltage
swell, voltage sag involving harmonics, voltage swell involving
harmonics, and voltage interruption. The non-linear interpolation
functions (NIFs) with fractal dimension (FD) make fractal patterns
more distinguishing between normal and abnormal voltage signals.
The classifier based on CRA discriminates the disturbance events in a
power system. Compared with the wavelet neural networks, the test
results will show accurate discrimination, good robustness, and faster
processing time for detecting disturbing events.
Abstract: This paper investigates the fractals generated by the dynamical system of intuitionistic fuzzy contractions in the intuitionistic
fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the
standard intuitionistic fuzzy metric spaces by using the intuitionistic fuzzy Banach contraction theorem. In addition to that, we analyze
some results on intuitionistic fuzzy fractals in the standard intuitionistic fuzzy metric spaces with respect to the Hausdorff intuitionistic
fuzzy metrics.
Abstract: The fractal-shaped orifices are assumed to have a
significant effect on the pressure drop downstream pipe flow due to
their edge self-similarity shape which enhances the mixing
properties. Here, we investigate the pressure drop after these fractals
using a digital micro-manometer at different stations downstream a
turbulent flow pipe then a direct comparison has been made with the
pressure drop measured from regular orifices with the same flow
area. Our results showed that the fractal-shaped orifices have a
significant effect on the pressure drop downstream the flow. Also
the pressure drop measured across the fractal-shaped orifices is
noticed to be lower that that from ordinary orifices of the same flow
areas. This result could be important in designing piping systems
from point of view of losses consideration with the same flow
control area. This is promising to use the fractal-shaped orifices as
flowmeters as they can sense the pressure drop across them
accurately with minimum losses than the regular ones.
Abstract: Semiconductor nanomaterials like TiO2 nanoparticles
(TiO2-NPs) approximately less than 100 nm in diameter have become
a new generation of advanced materials due to their novel and
interesting optical, dielectric, and photo-catalytic properties. With the
increasing use of NPs in commerce, to date few studies have
investigated the toxicological and environmental effects of NPs.
Motivated by the importance of TiO2-NPs that may contribute to the
cancer research field especially from the treatment prospective
together with the fractal analysis technique, we have investigated the
effect of TiO2-NPs on colony morphology in the dark condition
using fractal dimension as a key morphological characterization
parameter. The aim of this work is mainly to investigate the cytotoxic
effects of TiO2-NPs in the dark on the growth of human cervical
carcinoma (HeLa) cell colonies from morphological aspect. The in
vitro studies were carried out together with the image processing
technique and fractal analysis. It was found that, these colonies were
abnormal in shape and size. Moreover, the size of the control
colonies appeared to be larger than those of the treated group. The
mean Df +/- SEM of the colonies in untreated cultures was
1.085±0.019, N= 25, while that of the cultures treated with TiO2-NPs
was 1.287±0.045. It was found that the circularity of the control
group (0.401±0.071) is higher than that of the treated group
(0.103±0.042). The same tendency was found in the diameter
parameters which are 1161.30±219.56 μm and 852.28±206.50 μm
for the control and treated group respectively. Possible explanation of
the results was discussed, though more works need to be done in
terms of the for mechanism aspects. Finally, our results indicate that
fractal dimension can serve as a useful feature, by itself or in
conjunction with other shape features, in the classification of cancer
colonies.
Abstract: In this paper, we study FPGA implementation of a
novel supra-optimal receiver diversity combining technique,
generalized maximal ratio combining (GMRC), for wireless
transmission over fading channels in SIMO systems. Prior
published results using ML-detected GMRC diversity signal
driven by BPSK showed superior bit error rate performance to
the widely used MRC combining scheme in an imperfect
channel estimation (ICE) environment. Under perfect channel
estimation conditions, the performance of GMRC and MRC
were identical. The main drawback of the GMRC study was
that it was theoretical, thus successful FPGA implementation
of it using pipeline techniques is needed as a wireless
communication test-bed for practical real-life situations.
Simulation results showed that the hardware implementation
was efficient both in terms of speed and area. Since diversity
combining is especially effective in small femto- and picocells,
internet-associated wireless peripheral systems are to
benefit most from GMRC. As a result, many spinoff
applications can be made to the hardware of IP-based 4th
generation networks.
Abstract: The overall objective of this paper is to retrieve soil
surfaces parameters namely, roughness and soil moisture related to
the dielectric constant by inverting the radar backscattered signal
from natural soil surfaces.
Because the classical description of roughness using statistical
parameters like the correlation length doesn't lead to satisfactory
results to predict radar backscattering, we used a multi-scale
roughness description using the wavelet transform and the Mallat
algorithm. In this description, the surface is considered as a
superposition of a finite number of one-dimensional Gaussian
processes each having a spatial scale. A second step in this study
consisted in adapting a direct model simulating radar backscattering
namely the small perturbation model to this multi-scale surface
description. We investigated the impact of this description on radar
backscattering through a sensitivity analysis of backscattering
coefficient to the multi-scale roughness parameters.
To perform the inversion of the small perturbation multi-scale
scattering model (MLS SPM) we used a multi-layer neural network
architecture trained by backpropagation learning rule. The inversion
leads to satisfactory results with a relative uncertainty of 8%.
Abstract: The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.
Abstract: The purpose of this paper is to present the fuzzy contraction
properties of the Hutchinson-Barnsley operator on the fuzzy
hyperspace with respect to the Hausdorff fuzzy metrics. Also we
discuss about the relationships between the Hausdorff fuzzy metrics
on the fuzzy hyperspaces. Our theorems generalize and extend some
recent results related with Hutchinson-Barnsley operator in the metric
spaces.
Abstract: Video-on-demand (VOD) is designed by using content delivery networks (CDN) to minimize the overall operational cost and to maximize scalability. Estimation of the viewing pattern (i.e., the relationship between the number of viewings and the ranking of VOD contents) plays an important role in minimizing the total operational cost and maximizing the performance of the VOD systems. In this paper, we have analyzed a large body of commercial VOD viewing data and found that the viewing rank distribution fits well with the parabolic fractal distribution. The weighted linear model fitting function is used to estimate the parameters (coefficients) of the parabolic fractal distribution. This paper presents an analytical basis for designing an optimal hierarchical VOD contents distribution system in terms of its cost and performance.
Abstract: The objective of this paper is to characterize the spontaneous Electroencephalogram (EEG) signals of four different motor imagery tasks and to show hereby a possible solution for the present binary communication between the brain and a machine ora Brain-Computer Interface (BCI). The processing technique used in this paper was the fractal analysis evaluated by the Critical Exponent Method (CEM). The EEG signal was registered in 5 healthy subjects,sampling 15 measuring channels at 1024 Hz.Each channel was preprocessed by the Laplacian space ltering so as to reduce the space blur and therefore increase the spaceresolution. The EEG of each channel was segmented and its Fractaldimension (FD) calculated. The FD was evaluated in the time interval corresponding to the motor imagery and averaged out for all the subjects (each channel). In order to characterize the FD distribution,the linear regression curves of FD over the electrodes position were applied. The differences FD between the proposed mental tasks are quantied and evaluated for each experimental subject. The obtained results of the proposed method are a substantial fractal dimension in the EEG signal of motor imagery tasks and can be considerably utilized as the multiple-states BCI applications.
Abstract: The present paper deals with problems related to the
possibilities to use fractal systems to solve some important scientific
and practical problems connected with filtering and separation of
aqueous phases from organic ones. For this purpose a special
separator have been designed. The reactor was filled with a porous
material with fractal dimension, which is an integral part of the set
for filtration and separation of emulsions. As a model emulsion
hexadecan mixture with water in equal quantities (1:1) was used. We
examined the hydrodynamics of the separation of the emulsion at
different rates of submission of the entrance of the reactor.
Abstract: Successive event of explosion earthquake and harmonic tremor recorded at Semeru volcano were analyzed to investigate the dynamical system regarding to their eruptive mechanism. The eruptive activity at Semeru volcano East Java, Indonesia is intermittent emission of ash and bombs with Strombolian style which occurred at interval of 15 to 45 minutes. The explosive eruptions accompanied by explosion earthquakes and followed by volcanic tremor which generated by continuous emission of volcanic ash. The spectral and Lyapunov exponent of successive event of explosion and harmonic tremor were analyzed. Peak frequencies of explosion earthquakes range 1.2 to 1.9 Hz and those of the harmonic tremor have peak frequency range 1.5 — 2.2 Hz. The phase space is reconstructed and evaluated based on the Lyapunov exponents. Harmonic tremors have smaller Lyapunov exponent than explosion earthquakes. It can be considerably as correlated complexity of the mechanism from the variance of spectral and fractal dimension and can be concluded that the successive event of harmonic tremor and explosions are chaotic.
Abstract: In this paper, a fractional-order FIR differentiator
design method using the differential evolution (DE) algorithm is
presented. In the proposed method, the FIR digital filter is designed to
meet the frequency response of a desired fractal-order differentiator,
which is evaluated in the frequency domain. To verify the design
performance, another design method considered in the time-domain is
also provided. Simulation results reveal the efficiency of the proposed
method.
Abstract: The colonic tissue is a complicated dynamic system
and the colonic activities it generates are composed of irregular
segmental waves, which are referred to as erratic fluctuations or spikes.
They are also highly irregular with subunit fractal structure. The
traditional time-frequency domain statistics like the averaged
amplitude, the motility index and the power spectrum, etc. are
insufficient to describe such fluctuations. Thus the fractal
box-counting dimension is proposed and the fractal scaling behaviors
of the human colonic pressure activities under the physiological
conditions are studied. It is shown that the dimension of the resting
activity is smaller than that of the normal one, whereas the clipped
version, which corresponds to the activity of the constipation patient,
shows with higher fractal dimension. It may indicate a practical
application to assess the colonic motility, which is often indicated by
the colonic pressure activity.
Abstract: A nucleotide sequence can be expressed as a numerical sequence when each nucleotide is assigned its proton number. A resulting gene numerical sequence can be investigated for its fractal dimension in terms of evolution and chemical properties for comparative studies. We have investigated such nucleotide fluctuation in the 16S rRNA gene of archaea thermophiles. The studied archaea thermophiles were archaeoglobus fulgidus, methanothermobacter thermautotrophicus, methanocaldococcus jannaschii, pyrococcus horikoshii, and thermoplasma acidophilum. The studied five archaea-euryarchaeota thermophiles have fractal dimension values ranging from 1.93 to 1.97. Computer simulation shows that random sequences would have an average of about 2 with a standard deviation about 0.015. The fractal dimension was found to correlate (negative correlation) with the thermophile-s optimal growth temperature with R2 value of 0.90 (N =5). The inclusion of two aracheae-crenarchaeota thermophiles reduces the R2 value to 0.66 (N = 7). Further inclusion of two bacterial thermophiles reduces the R2 value to 0.50 (N =9). The fractal dimension is correlated (positive) to the sequence GC content with an R2 value of 0.89 for the five archaea-euryarchaeota thermophiles (and 0.74 for the entire set of N = 9), although computer simulation shows little correlation. The highest correlation (positive) was found to be between the fractal dimension and di-nucleotide Shannon entropy. However Shannon entropy and sequence GC content were observed to correlate with optimal growth temperature having an R2 of 0.8 (negative), and 0.88 (positive), respectively, for the entire set of 9 thermophiles; thus the correlation lacks species specificity. Together with another correlation study of bacterial radiation dosage with RecA repair gene sequence fractal dimension, it is postulated that fractal dimension analysis is a sensitive tool for studying the relationship between genotype and phenotype among closely related sequences.
Abstract: We develop new nonlinear methods of
immunofluorescence analysis for a sensitive technology of
respiratory burst reaction of DNA fluorescence due to oxidative
activity in the peripheral blood neutrophils. Histograms in flow
cytometry experiments represent a fluorescence flashes frequency as
functions of fluorescence intensity. We used the Shannon-Weaver
index for definition of neutrophils- biodiversity and Hurst index for
definition of fractal-s correlations in immunofluorescence for
different donors, as the basic quantitative criteria for medical
diagnostics of health status. We analyze frequencies of flashes,
information, Shannon entropies and their fractals in
immunofluorescence networks due to reduction of histogram range.
We found the number of simplest universal correlations for
biodiversity, information and Hurst index in diagnostics and
classification of pathologies for wide spectra of diseases. In addition
is determined the clear criterion of a common immunity and human
health status in a form of yes/no answers type. These answers based
on peculiarities of information in immunofluorescence networks and
biodiversity of neutrophils. Experimental data analysis has shown the
existence of homeostasis for information entropy in oxidative activity
of DNA in neutrophil nuclei for all donors.
Abstract: The dispersion of heavy particles line in an isotropic
and incompressible three-dimensional turbulent flow has been
studied using the Kinematic Simulation techniques to find out the
evolution of the line fractal dimension. In this study, the fractal
dimension of the line is found for different cases of heavy particles
inertia (different Stokes numbers) in the absence of the particle
gravity with a comparison with the fractal dimension obtained in the
diffusion case of material line at the same Reynolds number. It can
be concluded for the dispersion of heavy particles line in turbulent
flow that the particle inertia affect the fractal dimension of a line
released in a turbulent flow for Stokes numbers 0.02 < St < 2. At the
beginning for small times, most of the different cases are not affected
by the inertia until a certain time, the particle response time τa, with
larger time as the particles inertia increases, the fractal dimension of
the line increases owing to the particles becoming more sensitive to
the small scales which cause the change in the line shape during its
journey.
Abstract: We review a knowledge extractor model in
constructing 3G Killer Applications. The success of 3G is essential
for Government as it became part of Telecommunications National
Strategy. The 3G wireless technologies may reach larger area and
increase country-s ICT penetration. In order to understand future
customers needs, the operators require proper information
(knowledge) lying inside. Our work approached future customers as
complex system where the complex knowledge may expose regular
behavior. The hidden information from 3G future customers is
revealed by using fractal-based questionnaires. Afterward, further
statistical analysis is used to match the results with operator-s
strategic plan. The developments of 3G applications also consider its
saturation time and further improvement of the application.
Abstract: Biological reactions of individuals of a testing animal
to toxic substance are unique and can be used as an indication of the
existing of toxic substance. However, to distinguish such phenomenon
need a very complicate system and even more complicate to analyze
data in 3 dimensional. In this paper, a system to evaluate in vitro
biological activities to acute toxicity of stochastic self-affine
non-stationary signal of 3D goldfish swimming by using fractal
analysis is introduced. Regular digital camcorders are utilized by
proposed algorithm 3DCCPC to effectively capture and construct 3D
movements of the fish. A Critical Exponent Method (CEM) has been
adopted as a fractal estimator. The hypothesis was that the swimming
of goldfish to acute toxic would show the fractal property which
related to the toxic concentration. The experimental results supported
the hypothesis by showing that the swimming of goldfish under the
different toxic concentration has fractal properties. It also shows that
the fractal dimension of the swimming related to the pH value of FD Ôëê
0.26pH + 0.05. With the proposed system, the fish is allowed to swim
freely in all direction to react to the toxic. In addition, the trajectories
are precisely evaluated by fractal analysis with critical exponent
method and hence the results exhibit with much higher degree of
confidence.