Search results for: time series local fractal properties

Authors: O. Boussoufi, K. Lamrini Uahabi, M. Atounti

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The main purpose of this paper is to calculate the fractal dimension of some Julia Sets and Mandelbrot Set in the Misiurewicz Points. Using Matlab to generate the Julia Sets images that match the Misiurewicz points and using a Fractal software, we were able to find different measures that characterize those fractals in textures and other features. We are actually focusing on fractal dimension and the error calculated by the software. When executing the given equation of regression or the log-log slope of image a Box Counting method is applied to the entire image, and chosen settings are available in a FracLAc Program. Finally, a comparison is done for each image corresponding to the area (boundary) where Misiurewicz Point is located.

Keywords: box counting, FracLac, fractal dimension, Julia Sets, Mandelbrot Set, Misiurewicz Points

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Authors: Kamal, Adil Ahmad

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Earthquakes are among the most versatile natural and dynamic processes, and hence a fractal model is considered to be the best representative of the same. We present a novel method to process and analyse information hidden in earthquake sequences using Fractal Dimensions and Iterative Function Systems (IFS). Spatial and temporal variations in the fractal dimensions of seismicity observed around the Indian peninsula in last 30 years are studied. This was used as a possible precursor before large earthquakes in the region. IFS images for observed seismicity in the Himalayan belt were also obtained. We scan the whole data set and coarse grain of a selected window to reduce it to four bins. A critical analysis of four-cornered chaos-game clearly shows that the spatial variation in earthquake occurrences in Himalayan range is not random. Two subzones of Himalaya have a tendency to follow each other in time.

Keywords: earthquakes, fractals, Himalaya, iterated function systems

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Authors: Adnan H. M. Al-Helali, Hamza A. Ali

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Growth of censorship and pervasive monitoring on the Internet, Steganography arises as a new means of achieving secret communication. Steganography is the art and science of embedding information within electronic media used by common applications and systems. Generally, hiding information of multimedia within images will change some of their properties that may introduce few degradation or unusual characteristics. This paper presents a new image steganography approach for hiding information of multimedia (images, text, and audio) using generated Mandelbrot Fractal image as a cover. The proposed technique has been extensively tested with different images. The results show that the method is a very secure means of hiding and retrieving steganographic information. Experimental results demonstrate that an effective improvement in the values of the Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE), Normalized Cross Correlation (NCC) and Image Fidelity (IF) over the previous techniques.

Keywords: fractal image, information hiding, Mandelbrot et fractal, steganography

Procedia PDF Downloads 539

Authors: Adnan H. M. Al-Helali, Hamza A. Ali

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The growth of censorship and pervasive monitoring on the Internet, Steganography arises as a new means of achieving secret communication. Steganography is the art and science of embedding information within electronic media used by common applications and systems. Generally, hiding information of multimedia within images will change some of their properties that may introduce few degradation or unusual characteristics. This paper presents a new image steganography approach for hiding information of multimedia (images, text, and audio) using generated Mandelbrot Fractal image as a cover. The proposed technique has been extensively tested with different images. The results show that the method is a very secure means of hiding and retrieving steganographic information. Experimental results demonstrate that an effective improvement in the values of the Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE), Normalized Cross Correlation (NCC), and Image Fidelity (IF) over the pervious techniques.

Keywords: fractal image, information hiding, Mandelbrot set fractal, steganography

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Authors: T. K. Dutta, K. K. Das, N. Dutta

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The salient feature of this paper is primarily concerned with Ricker’s population model: f(x)=x e^(r(1-x/k)), where r is the control parameter and k is the carrying capacity, and some fruitful results are obtained with the following objectives: 1) Determination of bifurcation values leading to a chaotic region, 2) Development of Statistical Methods and Analysis required for the measure of Fractal dimensions, 3) Calculation of various fractal dimensions. These results also help that the invariant probability distribution on the attractor, when it exists, provides detailed information about the long-term behavior of a dynamical system. At the end, some open problems are posed for further research.

Keywords: Feigenbaum universality, chaos, Lyapunov exponent, fractal dimensions

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Authors: Farhad Asadi, Mohammad Javad Mollakazemi, Aref Ghafouri

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Recent research in neural networks science and neuroscience for modeling complex time series data and statistical learning has focused mostly on learning from high input space and signals. Local linear models are a strong choice for modeling local nonlinearity in data series. Locally weighted projection regression is a flexible and powerful algorithm for nonlinear approximation in high dimensional signal spaces. In this paper, different learning scenario of one and two dimensional data series with different distributions are investigated for simulation and further noise is inputted to data distribution for making different disordered distribution in time series data and for evaluation of algorithm in locality prediction of nonlinearity. Then, the performance of this algorithm is simulated and also when the distribution of data is high or when the number of data is less the sensitivity of this approach to data distribution and influence of important parameter of local validity in this algorithm with different data distribution is explained.

Keywords: local nonlinear estimation, LWPR algorithm, online training method, locally weighted projection regression method

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Authors: Wullapa Wongsinlatam

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Back propagation algorithm (BP) is a widely used technique in artificial neural network and has been used as a tool for solving the time series problems, such as decreasing training time, maximizing the ability to fall into local minima, and optimizing sensitivity of the initial weights and bias. This paper proposes an improvement of a BP technique which is called IM-COH algorithm (IM-COH). By combining IM-COH algorithm with cuckoo search algorithm (CS), the result is cuckoo search improved control output hidden layer algorithm (CS-IM-COH). This new algorithm has a better ability in optimizing sensitivity of the initial weights and bias than the original BP algorithm. In this research, the algorithm of CS-IM-COH is compared with the original BP, the IM-COH, and the original BP with CS (CS-BP). Furthermore, the selected benchmarks, four time series samples, are shown in this research for illustration. The research shows that the CS-IM-COH algorithm give the best forecasting results compared with the selected samples.

Keywords: artificial neural networks, back propagation algorithm, time series, local minima problem, metaheuristic optimization

Procedia PDF Downloads 152

Authors: Lingge Tan, Hongpeng Xu, Jieun Yang, Maarten Hornikx

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Acoustic diffusers are important components in enhancing the quality of room acoustics. This paper provides a type of modular diffuser based on the Sierpinski Triangle of the plane and combines it with fractal theory to expand the effective frequency range. In numerical calculations and full-scale model experiments, the effect of fractal design elements on normal-incidence diffusion coefficients is examined. It is demonstrated the reasonable times of iteration of modules is three, and the coverage density is 58.4% in the design frequency from 125Hz to 4kHz.

Keywords: acoustic diffuser, fractal, Sierpinski-triangle, diffusion coefficient

Procedia PDF Downloads 151

Authors: Mitra Saberi, Saeideh Fakhari, Amir Karam, Ali Ahmadabadi

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Geomorphology is the scientific study of the characteristics of form and shape of the Earth's surface. The existence of types of landforms and their variation is mainly controlled by changes in the shape and position of land and topography. In fact, the interest and application of fractal issues in geomorphology is due to the fact that many geomorphic landforms have fractal structures and their formation and transformation can be explained by mathematical relations. The purpose of this study is to identify and analyze the fractal behavior of landforms of macro geomorphologic regions of Iran, as well as studying and analyzing topographic and landform characteristics based on fractal relationships. In this study, using the Iranian digital elevation model in the form of slopes, coefficients of deposition and alluvial fan, the fractal dimensions of the curves were calculated through the box counting method. The morphometric characteristics of the landforms and their fractal dimension were then calculated for 4criteria (height, slope, profile curvature and planimetric curvature) and indices (maximum, Average, standard deviation) using ArcMap software separately. After investigating their correlation with fractal dimension, two-way regression analysis was performed and the relationship between fractal dimension and morphometric characteristics of landforms was investigated. The results show that the fractal dimension in different pixels size of 30, 90 and 200m, topographic curves of different landform units of Iran including mountain, hill, plateau, plain of Iran, from1.06in alluvial fans to1.17in The mountains are different. Generally, for all pixels of different sizes, the fractal dimension is reduced from mountain to plain. The fractal dimension with the slope criterion and the standard deviation index has the highest correlation coefficient, with the curvature of the profile and the mean index has the lowest correlation coefficient, and as the pixels become larger, the correlation coefficient between the indices and the fractal dimension decreases.

Keywords: box counting method, fractal dimension, geomorphology, Iran, landform

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Authors: K. Geetha Ramesh, A. Ramachandraiah

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In an internal building space, daylight becomes a powerful source of illumination. The challenge therefore, is to develop means of utilizing both direct and diffuse natural light in buildings while maintaining and improving occupant's visual comfort, particularly at greater distances from the windows throwing daylight. The geometrical features of windows in a building have significant effect in providing daylight. The main goal of this research is to develop an innovative window geometry, which will effectively provide the daylight component adequately together with internal reflected component(IRC) and also the external reflected component(ERC), if any. This involves exploration of a light redirecting system using fractal geometry for windows, in order to penetrate and distribute daylight more uniformly to greater depths, minimizing heat gain and glare, and also to reduce building energy use substantially. Of late the creation of fractal geometrical window and the occurrence of daylight illuminance due to such windows is becoming an interesting study. The amount of daylight can change significantly based on the window geometry and sky conditions. This leads to the (i) exploration of various fractal patterns suitable for window designs, and (ii) quantification of the effect of chosen fractal window based on the relationship between the fractal pattern, size, orientation and glazing properties for optimizing daylighting. There are a lot of natural lighting applications able to predict the behaviour of a light in a room through a traditional opening - a regular window. The conventional prediction methodology involves the evaluation of the daylight factor, the internal reflected component and the external reflected component. Having evaluated the daylight illuminance level for a conventional window, the technical performance of a fractal window for an optimal daylighting is to be studied and compared with that of a regular window. The methodologies involved are highlighted in this paper.

Keywords: daylighting, fractal geometry, fractal window, optimization

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Authors: I. Zahraoui, J. Terhzaz, A. Errkik, El. H. Abdelmounim, A. Tajmouati, L. Abdellaoui, N. Ababssi, M. Latrach

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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.

Keywords: dual-band antenna, fractal antenna, GPS band, modified ground structure, sierpinski triangle, WiMAX band

Procedia PDF Downloads 445

Authors: I. Slim, H. Akkari, A. Ben Abdallah, I. Bhouri, M. Hedi Bedoui

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Osteoporosis is a common disease characterized by low bone mass and deterioration of micro-architectural bone tissue, which provokes an increased risk of fracture. This work treats the texture characterization of trabecular bone radiographs. The aim was to analyze according to clinical research a group of 174 subjects: 87 osteoporotic patients (OP) with various bone fracture types and 87 control cases (CC). To characterize osteoporosis, Fractal and MultiFractal (MF) methods were applied to images for features (attributes) extraction. In order to improve the results, a new method of MF spectrum based on the q-stucture function calculation was proposed and a combination of Fractal and MF attributes was used. The Support Vector Machines (SVM) was applied as a classifier to distinguish between OP patients and CC subjects. The features fusion (fractal and MF) allowed a good discrimination between the two groups with an accuracy rate of 96.22%.

Keywords: fractal, micro-architecture analysis, multifractal, osteoporosis, SVM

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Authors: Tak-Chung Fu, Ying-Kit Hung, Fu-Lai Chung

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In the field of time series data mining, the concept of the Perceptually Important Point (PIP) identification process is first introduced in 2001. This process originally works for financial time series pattern matching and it is then found suitable for time series dimensionality reduction and representation. Its strength is on preserving the overall shape of the time series by identifying the salient points in it. With the rise of Big Data, time series data contributes a major proportion, especially on the data which generates by sensors in the Internet of Things (IoT) environment. According to the nature of PIP identification and the successful cases, it is worth to further explore the opportunity to apply PIP in time series ‘Big Data’. However, the performance of PIP identification is always considered as the limitation when dealing with ‘Big’ time series data. In this paper, two distributed versions of PIP identification based on the Specialized Binary (SB) Tree are proposed. The proposed approaches solve the bottleneck when running the PIP identification process in a standalone computer. Improvement in term of speed is obtained by the distributed versions.

Keywords: distributed computing, performance analysis, Perceptually Important Point identification, time series data mining

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Authors: Achouri Fatima, Chouicha Kaddour

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The main parameters affecting the workability are the water content, particle size, and the total surface of the grains, as long as the mixing water begins by wetting the surface of the grains and then fills the voids between the grains to form entrapped water, the quantity of water remaining is called free water. The aim is to undertake a fractal approach through the relationship between the concrete formulation parameters and workability, to develop this approach a series of concrete taken from the literature was investigated by varying formulation parameters such as G / S, the quantity of cement C and the quantity of mixing water E. We also call on other model as the model for the thickness of the water layer and model of the thickness of the paste layer to judge their relevance, hence the following results : the relevance of the model of the thickness of the water layer is considered relevant when there is a variation in the water quantity, the model of the thickness of the layer of the paste is only applicable if we consider that the paste is made with the grain value Dmax = 2.85: value from which we see a stable model.

Keywords: concrete, fractal method, paste thickness, water thickness, workability

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Authors: Eman A. Al-Hilo, Hawraa H. Al-Waelly

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In this work, fractal compression (FIC) technique is introduced based on using moment features to block indexing the zero-mean range-domain blocks. The moment features have been used to speed up the IFS-matching stage. Its moments ratio descriptor is used to filter the domain blocks and keep only the blocks that are suitable to be IFS matched with tested range block. The results of tests conducted on Lena picture and Cat picture (256 pixels, resolution 24 bits/pixel) image showed a minimum encoding time (0.89 sec for Lena image and 0.78 of Cat image) with appropriate PSNR (30.01dB for Lena image and 29.8 of Cat image). The reduction in ET is about 12% for Lena and 67% for Cat image.

Keywords: fractal gray level image, fractal compression technique, iterated function system, moments feature, zero-mean range-domain block

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Authors: Maria C. Mariani, Md Al Masum Bhuiyan, Osei K. Tweneboah, Hector G. Huizar

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This work is devoted to the study of modeling geophysical time series. A stochastic technique with time-varying parameters is used to forecast the volatility of data arising in geophysics. In this study, the volatility is defined as a logarithmic first-order autoregressive process. We observe that the inclusion of log-volatility into the time-varying parameter estimation significantly improves forecasting which is facilitated via maximum likelihood estimation. This allows us to conclude that the estimation algorithm for the corresponding one-step-ahead suggested volatility (with ±2 standard prediction errors) is very feasible since it possesses good convergence properties.

Keywords: Augmented Dickey Fuller Test, geophysical time series, maximum likelihood estimation, stochastic volatility model

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Authors: Saeedeh Shahbazkhany

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Cancer is a terrible disease that, if not diagnosed early, therapy can be difficult while it is easily medicable if it is diagnosed in early stages. So it is very important for cancer diagnosis that medical procedures are performed. In this paper we introduce a new method. In this method, we only need pictures of healthy cells and cancer cells. In fact, where we suspect cancer, we take a picture of cells or tissue in that area, and then take some pictures of the surrounding tissues. Then, fractal dimension of images are calculated and compared. Cancer can be easily detected by comparing the fractal dimension of images. In this method, we use Matlab software.

Keywords: Matlab software, fractal dimension, cancer, surrounding tissues, cells or tissue, new method

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Authors: Ognjen Vukovic

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Chern-Simons equation represents the cornerstone of quantum physics. The question that is often asked is if the aforementioned equation can be successfully applied to the interaction in international financial markets. By analysing the time series in financial theory, it is proved that Chern-Simons equation can be successfully applied to financial time-series. The aforementioned statement is based on one important premise and that is that the financial time series follow the fractional Brownian motion. All variants of Chern-Simons equation and theory are applied and analysed. Financial theory time series movement is, firstly, topologically analysed. The main idea is that exchange rate represents two-dimensional projections of three-dimensional Brownian motion movement. Main principles of knot theory and topology are applied to financial time series and setting is created so the Chern-Simons equation can be applied. As Chern-Simons equation is based on small particles, it is multiplied by the magnifying factor to mimic the real world movement. Afterwards, the following equation is optimised using Solver. The equation is applied to n financial time series in order to see if it can capture the interaction between financial time series and consequently explain it. The aforementioned equation represents a novel approach to financial time series analysis and hopefully it will direct further research.

Keywords: Brownian motion, Chern-Simons theory, financial time series, econophysics

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Authors: Ali Albadri

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Step band in an escalator moves in a cyclic periodic pattern. Similarly, most if not all of the components and sub-assemblies in the escalator operate in the same way. If you mark up one step in the step band of an escalator and stand next to the escalator, on the incline, to watch the marked-up step when it passes by, you ask yourself, does the marked up step behaves exactly the same way during each revolution when it passes you by again and again? We can say that; there is some similarity in this example and the example when an astronomer watches planets in the sky, and he or she asks himself or herself, does each planet intersects the plan of observation in the same position for every pantry rotation? For a fact, we know for the answer to the second example is no, because scientist, astronomers, and mathematicians have proven that planets deviate from their paths to take new paths during their planetary moves, albeit with minimal change. But what about the answer to the question in the first example? considering that there is increase in the wear and tear of components with time in the step, in the step band, in the tracks and in many other places in the escalator. There is also the accumulation of fatigue in the components and sub-assemblies. This research is part of many studies which we are conducting to address the answer for the question in the first example. We have been using the fractal dimension as a quantities tool and the Poincare map as a qualitative tool. This study has shown that the fractal dimension value and the shape and distribution of the orbits in the Poincare map has significant correlation with the quality of the mechanical components and sub-assemblies in the escalator.

Keywords: fractal dimension, Poincare map, rugby ball orbit, worm orbit

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Authors: Farhad Asadi, Mohammad Javad Mollakazemi

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In this paper, Bayesian online inference in models of data series are constructed by change-points algorithm, which separated the observed time series into independent series and study the change and variation of the regime of the data with related statistical characteristics. variation of statistical characteristics of time series data often represent separated phenomena in the some dynamical system, like a change in state of brain dynamical reflected in EEG signal data measurement or a change in important regime of data in many dynamical system. In this paper, prediction algorithm for studying change point location in some time series data is simulated. It is verified that pattern of proposed distribution of data has important factor on simpler and smother fluctuation of hazard rate parameter and also for better identification of change point locations. Finally, the conditions of how the time series distribution effect on factors in this approach are explained and validated with different time series databases for some dynamical system.

Keywords: time series, fluctuation in statistical characteristics, optimal learning, change-point algorithm

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Authors: C. Slim

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Traditional techniques for analyzing time series are based on the notion of stationarity of phenomena under study, but in reality most economic and financial series do not verify this hypothesis, which implies the implementation of specific tools for the detection of such behavior. In this paper, we study nonstationary non-seasonal time series tests in a non-exhaustive manner. We formalize the problem of nonstationary processes with numerical simulations and take stock of their statistical characteristics. The theoretical aspects of some of the most common unit root tests will be discussed. We detail the specification of the tests, showing the advantages and disadvantages of each. The empirical study focuses on the application of these tests to the exchange rate (USD/TND) and the Consumer Price Index (CPI) in Tunisia, in order to compare the Power of these tests with the characteristics of the series.

Keywords: stationarity, unit root tests, economic time series, ADF tests

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Authors: Amar Partap Singh Pharwaha, Shweta Rani

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This paper is aimed at proposing a rhombus shaped wearable fractal antenna for wireless communication systems. The geometrical descriptors of the antenna have been obtained using bacterial foraging optimization (BFO) for wide band operation. The method of moment based IE3D software has been used to simulate the antenna and observed that miniaturization of 13.08% has been achieved without degrading the resonating properties of the proposed antenna. An analysis with different substrates has also been done in order to evaluate the effectiveness of electrical permittivity on the presented structure. The proposed antenna has low profile, light weight and has successfully demonstrated wideband and multiband characteristics for wearable electronic applications.

Keywords: BFO, bandwidth, electrical permittivity, fractals, wearable antenna

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Authors: Wiem Gadri

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This study delves into the intriguing properties of Pisot and Salem numbers within the framework of formal Laurent series over finite fields, a domain where these numbers’ spectral charac-teristics, Λm(β) and lm(β), have yet to be fully explored. Utilizing a methodological approach that combines algebraic number theory with the analysis of power series, we extend the foundational work of Erdos, Joo, and Komornik to this new setting. Our research uncovers bounds for lm(β), revealing how these depend on the degree of the minimal polynomial of β and thus offering a novel characterization of Pisot and Salem formal power series. The findings significantly contribute to our understanding of these numbers, highlighting their distribution and properties in the context of formal power series. This investigation not only bridges number theory with formal power series analysis but also sets the stage for further interdisciplinary research in these areas.

Keywords: Pisot numbers, Salem numbers, formal power series, over a finite field

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Authors: Ibrahim Alsendid, Rob Sturman, Benjamin Sharp

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In this paper, we consider a family of 2-dimensional nonlinear area-preserving transformations on the torus. A single parameter η varies between 0 and 1, taking the transformation from a hyperbolic toral automorphism to the “Cerbelli-Giona” map, a system known to exhibit multifractal properties. Here we study the multifractal properties of the family of maps. We apply a box-counting method by defining a grid of boxes Bi(δ), where i is the index and δ is the size of the boxes, to quantify the distribution of stable and unstable manifolds of the map. When the parameter is in the range 0.51< η <0.58 and 0.68< η <1 the map is ergodic; i.e., the unstable and stable manifolds eventually cover the whole torus, although not in a uniform distribution. For accurate numerical results, we require correspondingly accurate construction of the stable and unstable manifolds. Here we use the piecewise linearity of the map to achieve this, by computing the endpoints of line segments that define the global stable and unstable manifolds. This allows the generalized fractal dimension Dq, and spectrum of dimensions f(α), to be computed with accuracy. Finally, the intersection of the unstable and stable manifold of the map will be investigated and compared with the distribution of periodic points of the system.

Keywords: Discrete-time dynamical systems, Fractal geometry, Multifractal behaviour of the Perturbed map, Multifractal of Dynamical systems

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Authors: Ioannis Andrianakis, Vasileios Gkatas, Nikos Eleftheriadis, Alexios Ellinidis, Ermioni Avramidou

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pscmsForecasting is an open-source web service that implements a variety of time series forecasting algorithms and exposes them to the user via the ubiquitous HTTP protocol. It allows developers to enhance their applications by adding time series forecasting functionalities through an intuitive and easy-to-use interface. This paper provides some background on time series forecasting and gives details about the implemented algorithms, aiming to enhance the end user’s understanding of the underlying methods before incorporating them into their applications. A detailed description of the web service’s interface and its various parameterizations is also provided. Being an open-source project, pcsmsForecasting can also be easily modified and tailored to the specific needs of each application.

Keywords: time series, forecasting, web service, open source

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Authors: Beibit Karibayev, Akmaral Imanbayeva, Timur Namazbayev

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Currently, the small spacecraft (SSC) industry is experiencing a big boom in popularity. This is primarily due to ease of use, low cost and mobility. In addition, these programs can be implemented not only at the state level but also at the level of companies, universities and other organizations. For remote sensing of the Earth (ERS), small spacecraft with an orientation system is used. It is important to take into account here that a remote sensing device, for example, a camera for photographing the Earth's surface, must be directed at the Earth's surface. But this, at first glance, the limitation can be turned into an advantage using a patch antenna. This work proposed to use a patch antenna based on a unidirectional fractal in the SSC. The CST Microwave Studio software package was used for simulation and research. Copper (ε = 1.0) was chosen as the emitting element and reflector. The height of the substrate was 1.6 mm, the type of substrate material was FR-4 (ε = 4.3). The simulation was performed in the frequency range of 0 – 6 GHz. As a result of the research, a patch antenna based on fractal geometry was developed for ERS nanosatellites. The capabilities of these antennas are modeled and investigated. A method for calculating and modeling fractal geometry for patch antennas has been developed.

Keywords: antenna, earth remote sensing, fractal, small spacecraft

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Authors: Md Al Masum Bhuiyan, Maria C. Mariani, Osei K. Tweneboah

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In the present work, we develop a technique for estimating the volatility of financial time series by using stochastic differential equation. Taking the daily closing prices from developed and emergent stock markets as the basis, we argue that the incorporation of stochastic volatility into the time-varying parameter estimation significantly improves the forecasting performance via Maximum Likelihood Estimation. While using the technique, we see the long-memory behavior of data sets and one-step-ahead-predicted log-volatility with ±2 standard errors despite the variation of the observed noise from a Normal mixture distribution, because the financial data studied is not fully Gaussian. Also, the Ornstein-Uhlenbeck process followed in this work simulates well the financial time series, which aligns our estimation algorithm with large data sets due to the fact that this algorithm has good convergence properties.

Keywords: financial time series, maximum likelihood estimation, Ornstein-Uhlenbeck type models, stochastic volatility model

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Authors: C. Elavarasi, T. Shanmuganantham

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A coplanar waveguide (CPW) feed is presented, and comprising a split ring resonator (SRR) loaded fractal with water lily shape is used for multi band applications. The impedance matching of the antenna is determined by the number of Koch curve fractal unit cells. The antenna is designed on a FR4 substrate with a permittivity of ε_{r =} 4.4 and size of 14 x 16 x 1.6 mm³ to generate multi resonant mode at 3.8 GHz covering S band, 8.68 GHz at X band, 13.96 GHz at Ku band, and 19.74 GHz at K band with reflection coefficient better than -10 dB. Simulation results show that the antenna exhibits the desired voltage standing wave ratio (VSWR) level and radiation patterns across the wide frequency range. The fundamental parameters of the antenna such as return loss, VSWR, good radiation pattern with reasonable gain across the operating bands are obtained.

Keywords: fractal, metamaterial, split ring resonator, waterlily shape

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Authors: Muhammad Tariq, Hammad Tahir, Fawwad Mahmood Butt

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Purpose: This study attempts to examine the best forecasting methodologies in the time series. The time series forecasting models such as VAR, ARCH and the ARMA are considered for the analysis. Methodology: The Bench Marks or the parameters such as Adjusted R square, F-stats, Durban Watson, and Direction of the roots have been critically and empirically analyzed. The empirical analysis consists of time series data of Consumer Price Index and Closing Stock Price. Findings: The results show that the VAR model performed better in comparison to other models. Both the reliability and significance of VAR model is highly appreciable. In contrary to it, the ARCH model showed very poor results for forecasting. However, the results of ARMA model appeared double standards i.e. the AR roots showed that model is stationary and that of MA roots showed that the model is invertible. Therefore, the forecasting would remain doubtful if it made on the bases of ARMA model. It has been concluded that VAR model provides best forecasting results. Practical Implications: This paper provides empirical evidences for the application of time series forecasting model. This paper therefore provides the base for the application of best time series forecasting model.

Keywords: forecasting, time series, auto regression, ARCH, ARMA

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Authors: O. Delage, H. Bencherif, T. Portafaix, A. Bourdier

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The main purpose of time series analysis is to learn about the dynamics behind some time ordered measurement data. Two approaches are used in the literature to get a better knowledge of the dynamics contained in observation data sequences. The first of these approaches concerns time series decomposition, which is an important analysis step allowing patterns and behaviors to be extracted as components providing insight into the mechanisms producing the time series. As in many cases, time series are short, noisy, and non-stationary. To provide components which are physically meaningful, methods such as Empirical Mode Decomposition (EMD), Empirical Wavelet Transform (EWT) or, more recently, Empirical Adaptive Wavelet Decomposition (EAWD) have been proposed. The second approach is to reconstruct the dynamics underlying the time series as a trajectory in state space by mapping a time series into a set of Rᵐ lag vectors by using the method of delays (MOD). Takens has proved that the trajectory obtained with the MOD technic is equivalent to the trajectory representing the dynamics behind the original time series. This work introduces the singular spectrum decomposition (SSD), which is a new adaptive method for decomposing non-linear and non-stationary time series in narrow-banded components. This method takes its origin from singular spectrum analysis (SSA), a nonparametric spectral estimation method used for the analysis and prediction of time series. As the first step of SSD is to constitute a trajectory matrix by embedding a one-dimensional time series into a set of lagged vectors, SSD can also be seen as a reconstruction method like MOD. We will first give a brief overview of the existing decomposition methods (EMD-EWT-EAWD). The SSD method will then be described in detail and applied to experimental time series of observations resulting from total columns of ozone measurements. The results obtained will be compared with those provided by the previously mentioned decomposition methods. We will also compare the reconstruction qualities of the observed dynamics obtained from the SSD and MOD methods.

Keywords: time series analysis, adaptive time series decomposition, wavelet, phase space reconstruction, singular spectrum analysis

Procedia PDF Downloads 104