Abstract: All the geophysical phenomena including river
networks and flow time series are fractal events inherently and fractal
patterns can be investigated through their behaviors. A non-linear
system like a river basin can well be analyzed by a non-linear
measure such as the fractal analysis. A bilateral study is held on the
fractal properties of the river network and the river flow time series.
A moving window technique is utilized to scan the fractal properties
of them. Results depict both events follow the same strategy
regarding to the fractal properties. Both the river network and the
time series fractal dimension tend to saturate in a distinct value.
Abstract: In this work a new offline signature recognition system
based on Radon Transform, Fractal Dimension (FD) and Support Vector Machine (SVM) is presented. In the first step, projections of
original signatures along four specified directions have been performed using radon transform. Then, FDs of four obtained
vectors are calculated to construct a feature vector for each
signature. These vectors are then fed into SVM classifier for recognition of signatures. In order to evaluate the effectiveness of
the system several experiments are carried out. Offline signature
database from signature verification competition (SVC) 2004 is used
during all of the tests. Experimental result indicates that the proposed method achieved high accuracy rate in signature recognition.
Abstract: Genetic Algorithms (GAs) are direct searching
methods which require little information from design space. This
characteristic beside robustness of these algorithms makes them to be
very popular in recent decades. On the other hand, while this method
is employed, there is no guarantee to achieve optimum results. This
obliged designer to run such algorithms more than one time to
achieve more reliable results. There are many attempts to modify the
algorithms to make them more efficient. In this paper, by application
of fractal dimension (particularly, Box Counting Method), the
complexity of design space are established for determination of
mutation and crossover probabilities (Pm and Pc). This methodology
is followed by a numerical example for more clarification. It is
concluded that this modification will improve efficiency of GAs and
make them to bring about more reliable results especially for design
space with higher fractal dimensions.
Abstract: In this study, 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. The fractal dimension of
the line is found in the case of different particle gravity (in practice,
different values of particle drift velocity) in the presence of small
particle inertia with a comparison with that 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 gravity affect the fractal dimension of the line for
different particle gravity velocities in the range 0.2 < W < 2. With
the increase of the particle drift velocity, the fractal dimension of the
line decreases which may be explained as the particles pass many
scales in their journey in the direction of the gravity and the particles
trajectories do not affect by these scales at high particle drift
velocities.
Abstract: In this paper, Zinc Oxide (ZnO) thin films are deposited on glass substrate by sol-gel method. The ZnO thin films with well defined orientation were acquired by spin coating of zinc acetate dehydrate monoethanolamine (MEA), de-ionized water and isopropanol alcohol. These films were pre-heated at 275°C for 10 min and then annealed at 350°C, 450°C and 550°C for 80 min. The effect of annealing temperature and different thickness on structure and surface morphology of the thin films were verified by Atomic Force Microscopy (AFM). It was found that there was a significant effect of annealing temperature on the structural parameters of the films such as roughness exponent, fractal dimension and interface width. Thin films also were characterizied by X-ray Diffractometery (XRD) method. XRD analysis revealed that the annealed ZnO thin films consist of single phase ZnO with wurtzite structure and show the c-axis grain orientation. Increasing annealing temperature increased the crystallite size and the c-axis orientation of the film after 450°C. Also In this study, ZnO thin films in different thickness have been prepared by sol-gel method on the glass substrate at room temperature. The thicknesses of films are 100, 150 and 250 nm. Using fractal analysis, morphological characteristics of surface films thickness in amorphous state were investigated. The results show that with increasing thickness, surface roughness (RMS) and lateral correlation length (ξ) are decreased. Also, the roughness exponent (α) and growth exponent (β) were determined to be 0.74±0.02 and 0.11±0.02, respectively.
Abstract: In this paper, quantitative evaluation of ultrasonic Cscan
images through estimation of their Fractal Dimension (FD) is
discussed. Necessary algorithm for evaluation of FD of any 2-D
digitized image is implemented by developing a computer code. For
the evaluation purpose several C-scan images of the Kevlar
composite impacted by high speed bullet and glass fibre composite
having flaw in the form of inclusion is used. This analysis
automatically differentiates a C-scan image showing distinct damage
zone, from an image that contains no such damage.
Abstract: Migration in breast cancer cell wound healing assay
had been studied using image fractal dimension analysis. The
migration of MDA-MB-231 cells (highly motile) in a wound healing
assay was captured using time-lapse phase contrast video microscopy
and compared to MDA-MB-468 cell migration (moderately motile).
The Higuchi fractal method was used to compute the fractal
dimension of the image intensity fluctuation along a single pixel
width region parallel to the wound. The near-wound region fractal
dimension was found to decrease three times faster in the MDA-MB-
231 cells initially as compared to the less cancerous MDA-MB-468
cells. The inner region fractal dimension was found to be fairly
constant for both cell types in time and suggests a wound influence
range of about 15 cell layer. The box-counting fractal dimension
method was also used to study region of interest (ROI). The MDAMB-
468 ROI area fractal dimension was found to decrease
continuously up to 7 hours. The MDA-MB-231 ROI area fractal
dimension was found to increase and is consistent with the behavior
of a HGF-treated MDA-MB-231 wound healing assay posted in the
public domain. A fractal dimension based capacity index has been
formulated to quantify the invasiveness of the MDA-MB-231 cells in
the perpendicular-to-wound direction. Our results suggest that image
intensity fluctuation fractal dimension analysis can be used as a tool
to quantify cell migration in terms of cancer severity and treatment
responses.
Abstract: We present analysis of spatial patterns of generic
disease spread simulated by a stochastic long-range correlation SIR
model, where individuals can be infected at long distance in a power
law distribution. We integrated various tools, namely perimeter,
circularity, fractal dimension, and aggregation index to characterize
and investigate spatial pattern formations. Our primary goal was to
understand for a given model of interest which tool has an advantage
over the other and to what extent. We found that perimeter and
circularity give information only for a case of strong correlation–
while the fractal dimension and aggregation index exhibit the growth
rule of pattern formation, depending on the degree of the correlation
exponent (β). The aggregation index method used as an alternative
method to describe the degree of pathogenic ratio (α). This study may
provide a useful approach to characterize and analyze the pattern
formation of epidemic spreading
Abstract: In this paper, we have developed a method to
compute fractal dimension (FD) of discrete time signals, in the
time domain, by modifying the box-counting method. The size
of the box is dependent on the sampling frequency of the
signal. The number of boxes required to completely cover the
signal are obtained at multiple time resolutions. The time
resolutions are made coarse by decimating the signal. The loglog
plot of total number of boxes required to cover the curve
versus size of the box used appears to be a straight line, whose
slope is taken as an estimate of FD of the signal. The results
are provided to demonstrate the performance of the proposed
method using parametric fractal signals. The estimation
accuracy of the method is compared with that of Katz, Sevcik,
and Higuchi methods. In addition, some properties of the FD
are discussed.
Abstract: Diffuse viral encephalitis may lack fever and other cardinal signs of infection and hence its distinction from other acute encephalopathic illnesses is challenging. Often, the EEG changes seen routinely are nonspecific and reflect diffuse encephalopathic changes only. The aim of this study was to use nonlinear dynamic mathematical techniques for analyzing the EEG data in order to look for any characteristic diagnostic patterns in diffuse forms of encephalitis.It was diagnosed on clinical, imaging and cerebrospinal fluid criteria in three young male patients. Metabolic and toxic encephalopathies were ruled out through appropriate investigations. Digital EEGs were done on the 3rd to 5th day of onset. The digital EEGs of 5 male and 5 female age and sex matched healthy volunteers served as controls.Two sample t-test indicated that there was no statistically significant difference between the average values in amplitude between the two groups. However, the standard deviation (or variance) of the EEG signals at FP1-F7 and FP2-F8 are significantly higher for the patients than the normal subjects. The regularisation dimension is significantly less for the patients (average between 1.24-1.43) when compared to the normal persons (average between 1.41-1.63) for the EEG signals from all locations except for the Fz-Cz signal. Similarly the wavelet dimension is significantly less (P = 0.05*) for the patients (1.122) when compared to the normal person (1.458). EEGs are subdued in the case of the patients with presence of uniform patterns, manifested in the values of regularisation and wavelet dimensions, when compared to the normal person, indicating a decrease in chaotic nature.
Abstract: This paper presents a new method of analog fault diagnosis based on back-propagation neural networks (BPNNs) using wavelet decomposition and fractal dimension as preprocessors. The proposed method has the capability to detect and identify faulty components in an analog electronic circuit with tolerance by analyzing its impulse response. Using wavelet decomposition to preprocess the impulse response drastically de-noises the inputs to the neural network. The second preprocessing by fractal dimension can extract unique features, which are the fed to a neural network as inputs for further classification. A comparison of our work with [1] and [6], which also employs back-propagation (BP) neural networks, reveals that our system requires a much smaller network and performs significantly better in fault diagnosis of analog circuits due to our proposed preprocessing techniques.