Abstract: One of research issues in social network analysis is to
evaluate the position/importance of users in social networks. As the
information diffusion in social network is evolving, it seems difficult
to evaluate the importance of users using traditional approaches. In
this paper, we propose an evaluation approach for user importance
with fractal view in social networks. In this approach, the global importance
(Fractal Importance) and the local importance (Topological
Importance) of nodes are considered. The basic idea is that the bigger
the product of fractal importance and topological importance of a
node is, the more important of the node is. We devise the algorithm
called TFRank corresponding to the proposed approach. Finally, we
evaluate TFRank by experiments. Experimental results demonstrate
our TFRank has the high correlations with PageRank algorithm
and potential ranking algorithm, and it shows the effectiveness and
advantages of our approach.
Abstract: Since 1984 many schemes have been proposed for
digital signature protocol, among them those that based on discrete
log and factorizations. However a new identification scheme based
on iterated function (IFS) systems are proposed and proved to be
more efficient. In this study the proposed identification scheme is
transformed into a digital signature scheme by using a one way hash
function. It is a generalization of the GQ signature schemes. The
attractor of the IFS is used to obtain public key from a private one,
and in the encryption and decryption of a hash function. Our aim is
to provide techniques and tools which may be useful towards
developing cryptographic protocols. Comparisons between the
proposed scheme and fractal digital signature scheme based on RSA
setting, as well as, with the conventional Guillou-Quisquater
signature, and RSA signature schemes is performed to prove that, the
proposed scheme is efficient and with high performance.
Abstract: L-system is a tool commonly used for modeling and simulating the growth of fractal plants. The aim of this paper is to join some problems of the computational geometry with the fractal geometry by using the L-system technique to generate fractal plant in 3D. L-system constructs the fractal structure by applying rewriting rules sequentially and this technique depends on recursion process with large number of iterations to get different shapes of 3D fractal plants. Instead, it was reiterated a specific number of iterations up to three iterations. The vertices generated from the last stage of the Lsystem rewriting process are used as input to the triangulation algorithm to construct the triangulation shape of these vertices. The resulting shapes can be used as covers for the architectural objects and in different computer graphics fields. The paper presents a gallery of triangulation forms which application in architecture creates an alternative for domes and other traditional types of roofs.
Abstract: In this paper a hybrid technique of Genetic Algorithm
and Simulated Annealing (HGASA) is applied for Fractal Image
Compression (FIC). With the help of this hybrid evolutionary
algorithm effort is made to reduce the search complexity of matching
between range block and domain block. The concept of Simulated
Annealing (SA) is incorporated into Genetic Algorithm (GA) in order
to avoid pre-mature convergence of the strings. One of the image
compression techniques in the spatial domain is Fractal Image
Compression but the main drawback of FIC is that it involves more
computational time due to global search. In order to improve the
computational time along with acceptable quality of the decoded
image, HGASA technique has been proposed. Experimental results
show that the proposed HGASA is a better method than GA in terms
of PSNR for Fractal image Compression.
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: Electrophysiological signals were recorded from primary cultures of dissociated rat cortical neurons coupled to Micro-Electrode Arrays (MEAs). The neuronal discharge patterns may change under varying physiological and pathological conditions. For this reason, we developed a new burst detection method able to identify bursts with peculiar features in different experimental conditions (i.e. spontaneous activity and under the effect of specific drugs). The main feature of our algorithm (i.e. Burst On Hurst), based on the auto-similarity or fractal property of the recorded signal, is the independence from the chosen spike detection method since it works directly on the raw data.
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: Medical imaging uses the advantage of digital
technology in imaging and teleradiology. In teleradiology systems
large amount of data is acquired, stored and transmitted. A major
technology that may help to solve the problems associated with the
massive data storage and data transfer capacity is data compression
and decompression. There are many methods of image compression
available. They are classified as lossless and lossy compression
methods. In lossy compression method the decompressed image
contains some distortion. Fractal image compression (FIC) is a lossy
compression method. In fractal image compression an image is
coded as a set of contractive transformations in a complete metric
space. The set of contractive transformations is guaranteed to
produce an approximation to the original image. In this paper FIC is
achieved by PIFS using quadtree partitioning. PIFS is applied on
different images like , Ultrasound, CT Scan, Angiogram, X-ray,
Mammograms. In each modality approximately twenty images are
considered and the average values of compression ratio and PSNR
values are arrived. In this method of fractal encoding, the
parameter, tolerance factor Tmax, is varied from 1 to 10, keeping the
other standard parameters constant. For all modalities of images the
compression ratio and Peak Signal to Noise Ratio (PSNR) are
computed and studied. The quality of the decompressed image is
arrived by PSNR values. From the results it is observed that the
compression ratio increases with the tolerance factor and
mammogram has the highest compression ratio. The quality of the
image is not degraded upto an optimum value of tolerance factor,
Tmax, equal to 8, because of the properties of fractal compression.
Abstract: Natural resources management including water resources requires reliable estimations of time variant environmental parameters. Small improvements in the estimation of environmental parameters would result in grate effects on managing decisions. Noise reduction using wavelet techniques is an effective approach for preprocessing of practical data sets. Predictability enhancement of the river flow time series are assessed using fractal approaches before and after applying wavelet based preprocessing. Time series correlation and persistency, the minimum sufficient length for training the predicting model and the maximum valid length of predictions were also investigated through a fractal assessment.
Abstract: Chaos and fractals are novel fields of physics and mathematics showing up a new way of universe viewpoint and creating many ideas to solve several present problems. In this paper, a novel algorithm based on the chaotic sequence generator with the highest ability to adapt and reach the global optima is proposed. The adaptive ability of proposal algorithm is flexible in 2 steps. The first one is a breadth-first search and the second one is a depth-first search. The proposal algorithm is examined by 2 functions, the Camel function and the Schaffer function. Furthermore, the proposal algorithm is applied to optimize training Multilayer Neural Networks.
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: The linear methods of heart rate variability analysis
such as non-parametric (e.g. fast Fourier transform analysis) and
parametric methods (e.g. autoregressive modeling) has become an
established non-invasive tool for marking the cardiac health, but their
sensitivity and specificity were found to be lower than expected with
positive predictive value
Abstract: Circle grid space filling plate is a flow conditioner with a fractal pattern and used to eliminate turbulence originating from pipe fittings in experimental fluid flow applications. In this paper, steady state, incompressible, swirling turbulent flow through circle grid space filling plate has been studied. The solution and the analysis were carried out using finite volume CFD solver FLUENT 6.2. Three turbulence models were used in the numerical investigation and their results were compared with the pressure drop correlation of BS EN ISO 5167-2:2003. The turbulence models investigated here are the standard k-ε, realizable k-ε, and the Reynolds Stress Model (RSM). The results showed that the RSM model gave the best agreement with the ISO pressure drop correlation. The effects of circle grids space filling plate thickness and Reynolds number on the flow characteristics have been investigated as well.
Abstract: A prototype model of an emulsion separator was
designed and manufactured. Generally, it is a cylinder filled with
different fractal modules. The emulsion was fed into the reactor by a
peristaltic pump through an inlet placed at the boundary between the
two phases. For hydrodynamic design and sizing of the reactor the
assumptions of the theory of filtration were used and methods to
describe the separation process were developed. Based on this
methodology and using numerical methods and software of Autodesk
the process is simulated in different operating modes. The basic
hydrodynamic characteristics - speed and performance for different
types of fractal systems and decisions to optimize the design of the
reactor were also defined.