Abstract: Applications of the Hausdorff space and its mappings
into tangent spaces are outlined, including their fractal dimensions
and self-similarities. The paper details this theory set up and further
describes virtualizations and atomization of manufacturing processes.
It demonstrates novel concurrency principles that will guide
manufacturing processes and resources configurations. Moreover,
varying levels of details may be produced by up folding and breaking
down of newly introduced generic models. This choice of layered
generic models for units and systems aspects along specific aspects
allows research work in parallel to other disciplines with the same
focus on all levels of detail. More credit and easier access are granted
to outside disciplines for enriching manufacturing grounds. Specific
mappings and the layers give hints for chances for interdisciplinary
outcomes and may highlight more details for interoperability
standards, as already worked on the international level. The new rules
are described, which require additional properties concerning all
involved entities for defining distributed decision cycles, again on the
base of self-similarity. All properties are further detailed and assigned
to a maturity scale, eventually displaying the smartness maturity of a
total shopfloor or a factory. The paper contributes to the intensive
ongoing discussion in the field of intelligent distributed
manufacturing and promotes solid concepts for implementations of
Cyber Physical Systems and the Internet of Things into
manufacturing industry, like industry 4.0, as discussed in German-speaking
countries.
Abstract: Modeling and forecasting dynamics of rainfall
occurrences constitute one of the major topics, which have been
largely treated by statisticians, hydrologists, climatologists and many
other groups of scientists. In the same issue, we propose, in the
present paper, a new hybrid method, which combines Extreme
Values and fractal theories. We illustrate the use of our methodology
for transformed Emberger Index series, constructed basing on data
recorded in Oujda (Morocco).
The index is treated at first by Peaks Over Threshold (POT)
approach, to identify excess observations over an optimal threshold u.
In the second step, we consider the resulting excess as a fractal object
included in one dimensional space of time. We identify fractal
dimension by the box counting. We discuss the prospect descriptions
of rainfall data sets under Generalized Pareto Distribution, assured by
Extreme Values Theory (EVT). We show that, despite of the
appropriateness of return periods given by POT approach, the
introduction of fractal dimension provides accurate interpretation
results, which can ameliorate apprehension of rainfall occurrences.
Abstract: This paper presents a novel fractal antenna structure
proposed for UWB (Ultra – Wideband) applications. The frequency
band 3.1-10.6GHz released by FCC (Federal Communication
Commission) as the commercial operation of UWB has been chosen
as frequency range for this antenna based on coplanar waveguide
(CPW) feed and circular shapes fulfilled according to fractal
geometry. The proposed antenna is validated and designed by using
an FR4 substrate with overall area of 34x43 mm2. The simulated
results performed by CST-Microwave Studio and compared by ADS
(Advanced Design System) show good matching input impedance
with return loss less than -10dB between 2.9 GHz and 11 GHz.
Abstract: This work presents a new planar multiband antenna
based on fractal geometry. This structure is optimized and validated
into simulation by using CST-MW Studio. To feed this antenna we
have used a CPW line which makes it easy to be incorporated with
integrated circuits. The simulation results presents a good matching
input impedance and radiation pattern in the GSM band at 900 MHz
and ISM band at 2.4 GHz. The final structure is a dual band fractal
antenna with 70 x 70 mm² as a total area by using an FR4 substrate.
Abstract: This paper presents a novel design of a microstrip
fractal antenna based on the use of Sierpinski triangle shape, it’s
designed and simulated by using FR4 substrate in the operating
frequency bands (GPS, WiMAX), the design is a fractal antenna with
a modified ground structure. The proposed antenna is simulated and
validated by using CST Microwave Studio Software, the simulated
results presents good performances in term of radiation pattern and
matching input impedance.
Abstract: Mammography has been one of the most reliable
methods for early detection of breast cancer. There are different
lesions which are breast cancer characteristic such as
microcalcifications, masses, architectural distortions and bilateral
asymmetry. One of the major challenges of analysing digital
mammogram is how to extract efficient features from it for accurate
cancer classification. In this paper we proposed a hybrid feature
extraction method to detect and classify all four signs of breast
cancer. The proposed method is based on multiscale surrounding
region dependence method, Gabor filters, multi fractal analysis,
directional and morphological analysis. The extracted features are
input to self adaptive resource allocation network (SRAN) classifier
for classification. The validity of our approach is extensively
demonstrated using the two benchmark data sets Mammographic
Image Analysis Society (MIAS) and Digital Database for Screening
Mammograph (DDSM) and the results have been proved to be
progressive.
Abstract: A wireless sensor network (WSN) is a collection of
sensor nodes organized into a cooperative network. These nodes
communicate through a wireless antenna. Reduction in physical size
and multiband operation is an important requirement of WSN
antenna. Fractal antenna is used for miniaturization and multiband
operation. The self-similar or self-affine and space filling property of
fractal geometry increases the effective electrical length of the
antenna, reduces the size and make them frequency independent. This
paper elaborates on Dual band fractal antenna with Coplanar
Waveguide (CPW) feed for WSN. The proposed antenna is designed
on a FR4 substrate with the dimension of 27mm x 28.5mm x 1.6mm,
resonates at 2.4GHz and 5.2GHz with a return loss less than -10dB.
The design and simulation process is carried out using IE3D
simulation software. The simulated and measured results are found in
good agreement.
Abstract: A circularly polarized fractal boundary microstrip
antenna is presented. The sides of a square patch along x- axis, yaxis
are replaced with Minkowski and Koch curves correspondingly.
By using the fractal curves as edges, asymmetry in the structure is
created to excite two orthogonal modes for circular polarization (CP)
operation. The indentation factors of the fractal curves are optimized
for pure CP. The simulated results of the novel polyfractal antenna
are demonstrated.
Abstract: In this paper, we introduce R Iterated Function System
and employ the Hutchinson Barnsley theory (HB) to construct a
fractal set as its unique fixed point by using Reich contractions in a
complete b metric space. We discuss about well posedness of fixed
point problem for b metric space.
Abstract: BCI (Brain Computer Interface) is a communication machine that translates brain massages to computer commands. These machines with the help of computer programs can recognize the tasks that are imagined. Feature extraction is an important stage of the process in EEG classification that can effect in accuracy and the computation time of processing the signals. In this study we process the signal in three steps of active segment selection, fractal feature extraction, and classification. One of the great challenges in BCI applications is to improve classification accuracy and computation time together. In this paper, we have used student’s 2D sample t-statistics on continuous wavelet transforms for active segment selection to reduce the computation time. In the next level, the features are extracted from some famous fractal dimension estimation of the signal. These fractal features are Katz and Higuchi. In the classification stage we used ANFIS (Adaptive Neuro-Fuzzy Inference System) classifier, FKNN (Fuzzy K-Nearest Neighbors), LDA (Linear Discriminate Analysis), and SVM (Support Vector Machines). We resulted that active segment selection method would reduce the computation time and Fractal dimension features with ANFIS analysis on selected active segments is the best among investigated methods in EEG classification.
Abstract: With the ever-increasing need for wireless communication and the emergence of many systems, it is important to design broadband antennas to cover a wide frequency range. The aim of this paper is to design a broadband patch antenna, employing the three techniques of slotting, adding directly coupled parasitic elements, and fractal EBG structures. The bandwidth is improved from 9.32% to 23.77%. A wideband ranging from 4.15 GHz to 5.27 GHz is obtained. Also a comparative analysis of embedding EBG structures at different heights is also done. The composite effect of integrating these techniques in the design provides a simple and efficient method for obtaining low profile, broadband, high gain antenna. By the addition of parasitic elements the bandwidth was increased to only 18.04%. Later on by embedding EBG structures the bandwidth was increased up to 23.77%. The design is suitable for variety of wireless applications like WLAN and Radar Applications.
Abstract: To develop a reliable and cost effective communication platform for the telemedicine applications, novel antenna design has been presented using bacterial foraging optimization (BFO) technique. The proposed antenna geometry is achieved by etching a modified Koch curve fractal shape at the edges and a square shape slot at the center of the radiating element of a patch antenna. It has been found that the new antenna has achieved 43.79% size reduction and better resonating characteristic than the original patch. Representative results for both simulations and numerical validations are reported in order to assess the effectiveness of the developed methodology.
Abstract: We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.
Abstract: In this paper, we propose a new method to describe fractal shapes using parametric l-systems. First we introduce scaling factors in the production rules of the parametric l-systems grammars. Then we decorticate these grammars with scaling factors using turtle algebra to show the mathematical relation between l-systems and iterated function systems (IFS). We demonstrate that with specific values of the scaling factors, we find the exact relationship established by Prusinkiewicz and Hammel between l-systems and IFS.
Abstract: Analysis of heart rate variability (HRV) has become a
popular non-invasive tool for assessing the activities of autonomic
nervous system. Most of the methods were hired from techniques
used for time series analysis. Currently used methods are time
domain, frequency domain, geometrical and fractal methods. A new
technique, which searches for pattern repeatability in a time series, is
proposed for quantifying heart rate (HR) time series. These set of
indices, which are termed as pattern repeatability measure and
pattern repeatability ratio are able to distinguish HR data clearly
from noise and electroencephalogram (EEG). The results of analysis
using these measures give an insight into the fundamental difference
between the composition of HR time series with respect to EEG and
noise.
Abstract: This paper presents the effectiveness of artificial
intelligent technique to apply for pattern recognition and
classification of Partial Discharge (PD). Characteristics of PD signal
for pattern recognition and classification are computed from the
relation of the voltage phase angle, the discharge magnitude and the
repeated existing of partial discharges by using statistical and fractal
methods. The simplified fuzzy ARTMAP (SFAM) is used for pattern
recognition and classification as artificial intelligent technique. PDs
quantities, 13 parameters from statistical method and fractal method
results, are inputted to Simplified Fuzzy ARTMAP to train system
for pattern recognition and classification. The results confirm the
effectiveness of purpose technique.
Abstract: A new technique of topological multi-scale analysis is
introduced. By performing a clustering recursively to build a
hierarchy, and analyzing the co-scale and intra-scale similarities, an
Iterated Function System can be extracted from any data set. The study
of fractals shows that this method is efficient to extract
self-similarities, and can find elegant solutions the inverse problem of
building fractals. The theoretical aspects and practical
implementations are discussed, together with examples of analyses of
simple fractals.
Abstract: Shot boundary detection is a fundamental step for the organization of large video data. In this paper, we propose a new method for video gradual shots detection and classification, using advantages of fractal analysis and AIS-based classifier. Proposed features are “vertical intercept" and “fractal dimension" of each frame of videos which are computed using Fourier transform coefficients. We also used a classifier based on Clonal Selection Algorithm. We have carried out our solution and assessed it according to the TRECVID2006 benchmark dataset.
Abstract: Image compression is one of the most important
applications Digital Image Processing. Advanced medical imaging
requires storage of large quantities of digitized clinical data. Due to
the constrained bandwidth and storage capacity, however, a medical
image must be compressed before transmission and storage. There
are two types of compression methods, lossless and lossy. In Lossless
compression method the original image is retrieved without any
distortion. In lossy compression method, the reconstructed images
contain some distortion. Direct Cosine Transform (DCT) and Fractal
Image Compression (FIC) are types of lossy compression methods.
This work shows that lossy compression methods can be chosen for
medical image compression without significant degradation of the
image quality. In this work DCT and Fractal Compression using
Partitioned Iterated Function Systems (PIFS) are applied on different
modalities of images like CT Scan, Ultrasound, Angiogram, X-ray
and mammogram. Approximately 20 images are considered in each
modality and the average values of compression ratio and Peak
Signal to Noise Ratio (PSNR) are computed and studied. The quality
of the reconstructed image is arrived by the PSNR values. Based on
the results it can be concluded that the DCT has higher PSNR values
and FIC has higher compression ratio. Hence in medical image
compression, DCT can be used wherever picture quality is preferred
and FIC is used wherever compression of images for storage and
transmission is the priority, without loosing picture quality
diagnostically.
Abstract: Fractal analyses of successive event of explosion
earthquake and harmonic tremor recorded at Semeru volcano were
carried out to investigate the dynamical system regarding to their
generating mechanism. The explosive eruptions accompanied by
explosion earthquakes and following volcanic tremor which are
generated by continuous emission of volcanic ash. The fractal
dimension of successive event of explosion and harmonic tremor was
estimated by Critical Exponent Method (CEM). It was found that the
method yield a higher fractal dimension of explosion earthquakes and
gradually decrease during the occurrence of harmonic tremor, and can
be considerably as correlated complexity of the source mechanism
from the variance of fractal dimension.