scholarly journals Spatial Signal Analysis Based on Wave-Spectral Fractal Scaling: A Case of Urban Street Networks

2020 ◽  
Vol 11 (1) ◽  
pp. 87
Author(s):  
Yanguang Chen ◽  
Yuqing Long
Keyword(s):  
Signal Analysis ◽  
Fractal Theory ◽  
Scaling Law ◽  
Wave Spectrum ◽  
Ordinary Least Squares ◽  
Urban Traffic ◽  
Traffic Networks ◽  
Mathematical Methods ◽  
Spatiotemporal Signal ◽  
Analytical Approaches

A number of mathematical methods have been developed to make temporal signal analyses based on time series. However, no effective method for spatial signal analysis, which are as important as temporal signal analyses for geographical systems, has been devised. Nonstationary spatial and temporal processes are associated with nonlinearity, and cannot be effectively analyzed by conventional analytical approaches. Fractal theory provides a powerful tool for exploring spatial complexity and is helpful for spatio-temporal signal analysis. This paper is devoted to developing an approach for analyzing spatial signals of geographical systems by means of wave-spectrum scaling. The traffic networks of 10 Chinese cities are taken as cases for positive studies. Fast Fourier transform (FFT) and ordinary least squares (OLS) regression methods are employed to calculate spectral exponents. The results show that the wave-spectrum density distribution of all these urban traffic networks follows scaling law, and that the spectral scaling exponents can be converted into fractal dimension values. Using the fractal parameters, we can make spatial analyses for the geographical signals. The wave-spectrum scaling methods can be applied to both self-similar fractal signals and self-affine fractal signals in the geographical world. This study has implications for the further development of fractal-based spatiotemporal signal analysis in the future.

scholarly journals MATHEMATICAL METHODS IN CYBER SECURITY: FRACTALS AND THEIR APPLICATIONS IN INFORMATION AND CYBER SECURITY

2019 ◽  
pp. 31-39
Author(s):  
Svitlana Shevchenko ◽  
Yulia Zhdanovа ◽  
Svitlana Spasiteleva ◽  
Olena Negodenko ◽  
Nataliia Mazur ◽  
...  
Keyword(s):  
Fractal Analysis ◽  
Cyber Security ◽  
Fractal Theory ◽  
Research Work ◽  
Digital Processing ◽  
Information Protection ◽  
Mathematical Apparatus ◽  
Mathematical Methods ◽  
Fractal Modeling ◽  
Encryption Algorithms

The article deals with the application of modern mathematical apparatus in information and cyber security namely fractal analysis. The choice of fractal modeling for the protection of information in the process of its digital processing is grounded. Based on scientific sources, the basic definitions of the research are analyzed: fractal, its dimension and basic properties used in the process of information protection. The basic types of fractals (geometric, algebraic, statistical) are presented and the most famous of them are described. The historical perspective of the development of fractal theory is conducted. Different approaches to the application of fractal theory in information and cyber security have been reviewed. Among them are: the use of fractal analysis in encryption algorithms; development of a method of protecting documents with latent elements based on fractals; modeling the security system of each automated workplace network using a set of properties that can be represented as fractals. The considered approaches to the application of fractal analysis in information and cyber security can be used in the preparation of specialists in the process of research work or diploma work.

COMPRESSIVE STRENGTH OF FRACTAL-TEXTURED FOAMED CONCRETE

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940003 ◽  
Author(s):  
Y. CHEN ◽  
Y. F. XU
Keyword(s):  
Compressive Strength ◽  
Fractal Dimension ◽  
Porous Structure ◽  
Fractal Theory ◽  
Scaling Law ◽  
Weight Ratio ◽  
High Strength ◽  
Labor Cost ◽  
Fractal Model ◽  
Foamed Concrete

Foamed concrete possesses characteristics such as high strength-to-weight ratio and low density, and widely used to reduce dead loads on the structure and foundation, contributes to energy conservation, and lowers the labor cost during construction. In this paper, the objective is to propose prediction relation for the compressive strength of foamed concrete by fractal theory. A theoretical relation was derived for the compressive strength relating to porosity based on the fractal model for foamed concrete. The proposed relation stands out compared to empirical model since it employs easily measurable parameter, the fractal dimension of porous structure in foamed concrete. The fractal dimension of porous structure can be calculated from the scaling law of the compressive strength of foamed concrete. The fractal model for porous structure serves as a simple and effective tool for predicting the compressive strength of foamed concrete because of its ease in application. The prediction relation of the compressive strength developed in this paper is found to match well with the measured strength.

A Fuzzy Logic Method of Traffic State Recognition on Urban Traffic Networks

2012 ◽  
Vol 546-547 ◽  
pp. 1071-1074
Author(s):  
Jian Ling Wang ◽  
Hong Bo Lai
Keyword(s):  
Fuzzy Logic ◽  
Traffic Flow ◽  
Urban Traffic ◽  
Traffic Networks ◽  
Traffic Condition ◽  
Time Length ◽  
Traffic State ◽  
Fuzzy Logic Method ◽  
Logic Method ◽  
Urban Traffic Networks

The study object is traffic flow on main road of urban traffic networks, the traffic condition is recognized by traffic flow theory and fuzzy logic method. The average space speed is a variable of the fact flow function, the road congestion degree is described by the ratio of fact flow and traffic capacity; the ratio of congestion time length and total time length is the congestion frequency. Considering congestion degree and congestion frequency, a fuzzy logic method is used to describe the traffic state by three grades: free, congestion and serious congestion. At last, the numerical example is given to analyze traffic state.

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