This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block co...This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block code share the propertyof linear correlation, the existing linear correlation-basedidentification method is invalid for this case. This drawback can becircumvented by introducing a novel multi-fractal spectrum-basedmethod. Simulation results show that the new method has highrobustness and under the same conditions of bit error, the lowerthe code rate, the higher the recognition rate. Thus, the methodhas significant potential for future application in engineering.展开更多
The multifractal formalism is shown to hold for a class of Moran measures supported on the Moran fractals associated with the sequences of which the frequency of the letter exists.
There are many methods to calculate seismic fractal at present. However, there are still more or less questions to every method. In this paper, we introduce a new way to calculate seismic fractal-the minimal spanning ...There are many methods to calculate seismic fractal at present. However, there are still more or less questions to every method. In this paper, we introduce a new way to calculate seismic fractal-the minimal spanning tree. We make an important improvement for this method. By studying some seismic events of four regions including Wushi, Wusu, Tangshan and Haicheng, we obtain that before the strong earthquake occurrence, the multi-fractal spectrum of the space-time distribution of earthquakes changes from centralized to loose. The result shows that the complexity of fractal structure and the inhomogeneity of the space-time distribution of earthquakes are both increasing. By studying the numerical simulation of point sets, we draw the conclusion that the physical essence of multi-fractal spectrums before and after a strong earthquake occurrence is a changing process from homogeneous to inhomogeneous, from simple to complex.展开更多
Several studies on earthquake occurrence and associated faulting have demonstrated that both phenomena have a scale-invariant behavior which can be analyzed by means of a set of non-integer dimensions （Dq） describin...Several studies on earthquake occurrence and associated faulting have demonstrated that both phenomena have a scale-invariant behavior which can be analyzed by means of a set of non-integer dimensions （Dq） describing their fractal properties and the calculation ofmulti-fractal spectra. It is the case that the behavior of these spectra is asymptotic at the ends of the variation interval of q, which is a real number that enters into the definition of the partition function of the dataset. The difference between the extreme values, called multi-fractal spectrum slope, is used to investigate the heterogeneity of the spatial distribution of earthquakes and fault systems. In this paper we focus on the Betic Cordillera, southeastern Spain, which is commonly considered the contact between the Eurasian and African plates and has an important seismic activity in the context of the Iberian Peninsula. Some of the most conspicuous Iberian earthquakes, such as the 1829 mb6.3 Torrevieja and the 1884 mb6.1 Alhama de Granada earthquakes occurred in this mountain range and both reached intensity X. The pre- sent work implies a new analysis based on the slope of multi-fractal spectra and referred to the historical seismicity of the re- gion, specifically b-value （frequency distribution of earthquakes respect to magnitude）, epicentral location, seismic energy and faulting. On this basis we propose a seismotectonic zonation that is contrasted with the stress state and the geodynamical evolution of the Betic Cordillera.展开更多
The discrete Fourier transform（DFT） is used for fractional Brownian motion（FBM） surface synthesis in tribology（i.e., contact, sliding, and sealing, etc）. However, the relationship between fractal parameters（fra...The discrete Fourier transform（DFT） is used for fractional Brownian motion（FBM） surface synthesis in tribology（i.e., contact, sliding, and sealing, etc）. However, the relationship between fractal parameters（fractal dimension and scale factor） and traditional parameters, the influence of fractal parameters on surface appearance, have not been deeply discussed yet. These lead to some kind of difficulty to ensure the synthesized surfaces with ideal fractal characteristic, required traditional parameters and geometric appearance. A quantitative relationship between fractal parameters and the root mean square deviation of surface （Sq） is derived based on the energy conservation property between the space and frequency domain of DFT. Under the stability assumption, the power spectrum of a FBM surface is composed of concentric circles strictly, a series of FBM surfaces with prescribed Sq could be synthesized with given fractal dimension, scale factor, and sampling numbers, but the ten-point height（Sz）, the skewness（Ssk） and the kurtosis（Sku） are still in random, where the probability distributions of Sz and Ssk are approximately normal distribution. Furthermore, by iterative searching, a surface with desired Abbott-Firestone curve could be obtained among those surfaces. An intuitive explanation for the influence of fractal dimension and scale factor on surface appearance is obtained by discussing the effects on the ratio of energy between high and low frequency components. Based on the relationship between Sq and surface energy, a filtering method of surface with controllable Sq is proposed. The proposed research ensures the synthesized surfaces possess ideal FBM properties with prescribed Sq, offers a method for selecting desired Abbott-Firestone curve of synthesized fractal surfaces, and makes it possible to control the Sq of surfaces after filtering.展开更多
Sedimentary cyclothems at different scales show formations’ fractal structure which can be reflected on logs. The slope of the power spectrum of log is related to the fractal dimension of formations. The fractal dime...Sedimentary cyclothems at different scales show formations’ fractal structure which can be reflected on logs. The slope of the power spectrum of log is related to the fractal dimension of formations. The fractal dimensions from two logs with similar vertical resolutions are the same. Using fractal interpolating algorithm density log can be reconstructed. The reconstructed log can be compared with core density in washout intervals.展开更多
Texture analysis is important in several image segmentation and classification problems. Different image textures manifest themselves by dissimilarity in both the property values and the spatial interrelationships of ...Texture analysis is important in several image segmentation and classification problems. Different image textures manifest themselves by dissimilarity in both the property values and the spatial interrelationships of their component texture primitives. We use this fact in a texture discrimination system. This paper focuses on how to apply texture operators based on co-occurrence matrix, texture filters and fractal dimension to the problem of object recognition and image segmentation.展开更多
The base sequence in genome was governed by some fundamental principles such as reverse-complement symmetry, multiple fractality and so on, and the analytical method of the genome structure, the “Sequence Spectrum Me...The base sequence in genome was governed by some fundamental principles such as reverse-complement symmetry, multiple fractality and so on, and the analytical method of the genome structure, the “Sequence Spectrum Method (SSM)”, based on the structural features of genomic DNA faithfully visualized these principles. This paper reported that the sequence spectrum in SSM closely reflected the biological phenomena of protein and DNA, and SSM could identify the interactive region of protein-protein and DNA-protein uniformly. In order to investigate the effectiveness of SSM we analyzed the several protein-protein and DNA-protein interaction published primarily in the genome of Saccharomyces cerevisiae. The method proposed here was based on the homology of sequence spectrum, and it advantageously and surprisingly used only base sequence of genome and did not require any other information, even information about the amino-acid sequence of protein. Eventually it was concluded that the fundamental principles in genome governed not only the static base sequence but also the dynamic function of protein and DNA.展开更多
基金supported by the National Natural Science Foundation of China(61171170) the Natural Science Foundation of Anhui Province(1408085QF115)
文摘This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block code share the propertyof linear correlation, the existing linear correlation-basedidentification method is invalid for this case. This drawback can becircumvented by introducing a novel multi-fractal spectrum-basedmethod. Simulation results show that the new method has highrobustness and under the same conditions of bit error, the lowerthe code rate, the higher the recognition rate. Thus, the methodhas significant potential for future application in engineering.
基金supported by the National Natural Science Foundation of China(Grant No.10171028)the Special for Major State Basic Research Projects of China.
文摘The multifractal formalism is shown to hold for a class of Moran measures supported on the Moran fractals associated with the sequences of which the frequency of the letter exists.
文摘There are many methods to calculate seismic fractal at present. However, there are still more or less questions to every method. In this paper, we introduce a new way to calculate seismic fractal-the minimal spanning tree. We make an important improvement for this method. By studying some seismic events of four regions including Wushi, Wusu, Tangshan and Haicheng, we obtain that before the strong earthquake occurrence, the multi-fractal spectrum of the space-time distribution of earthquakes changes from centralized to loose. The result shows that the complexity of fractal structure and the inhomogeneity of the space-time distribution of earthquakes are both increasing. By studying the numerical simulation of point sets, we draw the conclusion that the physical essence of multi-fractal spectrums before and after a strong earthquake occurrence is a changing process from homogeneous to inhomogeneous, from simple to complex.
基金The Ministry of Education and Science funded this study (project CGL2007-60535)sponsored by the Junta de Andalucía, Spain, through the Research Groups RNM-217 and RNM-024
文摘Several studies on earthquake occurrence and associated faulting have demonstrated that both phenomena have a scale-invariant behavior which can be analyzed by means of a set of non-integer dimensions （Dq） describing their fractal properties and the calculation ofmulti-fractal spectra. It is the case that the behavior of these spectra is asymptotic at the ends of the variation interval of q, which is a real number that enters into the definition of the partition function of the dataset. The difference between the extreme values, called multi-fractal spectrum slope, is used to investigate the heterogeneity of the spatial distribution of earthquakes and fault systems. In this paper we focus on the Betic Cordillera, southeastern Spain, which is commonly considered the contact between the Eurasian and African plates and has an important seismic activity in the context of the Iberian Peninsula. Some of the most conspicuous Iberian earthquakes, such as the 1829 mb6.3 Torrevieja and the 1884 mb6.1 Alhama de Granada earthquakes occurred in this mountain range and both reached intensity X. The pre- sent work implies a new analysis based on the slope of multi-fractal spectra and referred to the historical seismicity of the re- gion, specifically b-value （frequency distribution of earthquakes respect to magnitude）, epicentral location, seismic energy and faulting. On this basis we propose a seismotectonic zonation that is contrasted with the stress state and the geodynamical evolution of the Betic Cordillera.
基金supported by National Natural Science Foundation of China(Grant Nos.51175085,51205062)Fujian Provincial Natural Science Foundation of China(Grant Nos.2011J01299,2012J01206)Development Foundation for Science and Technology of Fuzhou University,China(Grant No.2011-XY-10)
文摘The discrete Fourier transform（DFT） is used for fractional Brownian motion（FBM） surface synthesis in tribology（i.e., contact, sliding, and sealing, etc）. However, the relationship between fractal parameters（fractal dimension and scale factor） and traditional parameters, the influence of fractal parameters on surface appearance, have not been deeply discussed yet. These lead to some kind of difficulty to ensure the synthesized surfaces with ideal fractal characteristic, required traditional parameters and geometric appearance. A quantitative relationship between fractal parameters and the root mean square deviation of surface （Sq） is derived based on the energy conservation property between the space and frequency domain of DFT. Under the stability assumption, the power spectrum of a FBM surface is composed of concentric circles strictly, a series of FBM surfaces with prescribed Sq could be synthesized with given fractal dimension, scale factor, and sampling numbers, but the ten-point height（Sz）, the skewness（Ssk） and the kurtosis（Sku） are still in random, where the probability distributions of Sz and Ssk are approximately normal distribution. Furthermore, by iterative searching, a surface with desired Abbott-Firestone curve could be obtained among those surfaces. An intuitive explanation for the influence of fractal dimension and scale factor on surface appearance is obtained by discussing the effects on the ratio of energy between high and low frequency components. Based on the relationship between Sq and surface energy, a filtering method of surface with controllable Sq is proposed. The proposed research ensures the synthesized surfaces possess ideal FBM properties with prescribed Sq, offers a method for selecting desired Abbott-Firestone curve of synthesized fractal surfaces, and makes it possible to control the Sq of surfaces after filtering.
文摘Sedimentary cyclothems at different scales show formations’ fractal structure which can be reflected on logs. The slope of the power spectrum of log is related to the fractal dimension of formations. The fractal dimensions from two logs with similar vertical resolutions are the same. Using fractal interpolating algorithm density log can be reconstructed. The reconstructed log can be compared with core density in washout intervals.
文摘Texture analysis is important in several image segmentation and classification problems. Different image textures manifest themselves by dissimilarity in both the property values and the spatial interrelationships of their component texture primitives. We use this fact in a texture discrimination system. This paper focuses on how to apply texture operators based on co-occurrence matrix, texture filters and fractal dimension to the problem of object recognition and image segmentation.
文摘The base sequence in genome was governed by some fundamental principles such as reverse-complement symmetry, multiple fractality and so on, and the analytical method of the genome structure, the “Sequence Spectrum Method (SSM)”, based on the structural features of genomic DNA faithfully visualized these principles. This paper reported that the sequence spectrum in SSM closely reflected the biological phenomena of protein and DNA, and SSM could identify the interactive region of protein-protein and DNA-protein uniformly. In order to investigate the effectiveness of SSM we analyzed the several protein-protein and DNA-protein interaction published primarily in the genome of Saccharomyces cerevisiae. The method proposed here was based on the homology of sequence spectrum, and it advantageously and surprisingly used only base sequence of genome and did not require any other information, even information about the amino-acid sequence of protein. Eventually it was concluded that the fundamental principles in genome governed not only the static base sequence but also the dynamic function of protein and DNA.
