Surface Fractal Dimension of Bentonite and its Application in Calculation of Swelling Deformation
NASA Astrophysics Data System (ADS)
Xiang, G. S.; Xu, Y. F.; Jiang, H.
2014-09-01
The correlation between the void ratio of swelled montmorillonite and the vertical overburden pressure can be expressed as {e}{ m} = Kp{ s}{D{ s}-3}. The surface fractal dimension Ds of five bentonites were estimated from the swelling deformation tests according to this fractal correlation. The reliability of surface fractal dimension obtained from the swelling deformation test was confirmed by nitrogen adsorption test, with identical values of surface fractal dimension obtained from both tests. The surface fractal dimension can also be used to estimate the swelling deformation of bentonite, after calculating the swelling coefficient K from the parameters of diffuse double layer (DDL) model in the osmotic swelling phase. Comparison of the model predictions with a number of experimental results on swelling deformation of both Na dominant and Ca dominant bentonites suggests that the surface fractal model works excellent in the cases tested.
The Three-Point Sinuosity Method for Calculating the Fractal Dimension of Machined Surface Profile
NASA Astrophysics Data System (ADS)
Zhou, Yuankai; Li, Yan; Zhu, Hua; Zuo, Xue; Yang, Jianhua
2015-04-01
The three-point sinuosity (TPS) method is proposed to calculate the fractal dimension of surface profile accurately. In this method, a new measure, TPS is defined to present the structural complexity of fractal curves, and has been proved to follow the power law. Thus, the fractal dimension can be calculated through the slope of the fitted line in the log-log plot. The Weierstrass-Mandelbrot (W-M) fractal curves, as well as the real surface profiles obtained by grinding, sand blasting and turning, are used to validate the effectiveness of the proposed method. The calculation values are compared to those obtained from root-mean-square (RMS) method, box-counting (BC) method and variation method. The results show that the TPS method has the widest scaling region, the least fit error and the highest accuracy among the methods examined, which demonstrates that the fractal characteristics of the fractal curves can be well revealed by the proposed method.
The Calculation of Fractal Dimension in the Presence of Non-Fractal Clutter
NASA Technical Reports Server (NTRS)
Herren, Kenneth A.; Gregory, Don A.
1999-01-01
The area of information processing has grown dramatically over the last 50 years. In the areas of image processing and information storage the technology requirements have far outpaced the ability of the community to meet demands. The need for faster recognition algorithms and more efficient storage of large quantities of data has forced the user to accept less than lossless retrieval of that data for analysis. In addition to clutter that is not the object of interest in the data set, often the throughput requirements forces the user to accept "noisy" data and to tolerate the clutter inherent in that data. It has been shown that some of this clutter, both the intentional clutter (clouds, trees, etc) as well as the noise introduced on the data by processing requirements can be modeled as fractal or fractal-like. Traditional methods using Fourier deconvolution on these sources of noise in frequency space leads to loss of signal and can, in many cases, completely eliminate the target of interest. The parameters that characterize fractal-like noise (predominately the fractal dimension) have been investigated and a technique to reduce or eliminate noise from real scenes has been developed. Examples of clutter reduced images are presented.
Calculation of multi-fractal dimensions in spin chains
Atas, Y. Y.; Bogomolny, E.
2014-01-01
It was demonstrated in Atas & Bogomolny (2012 Phys. Rev. E 86, 021104) that the ground-state wave functions for a large variety of one-dimensional spin- models are multi-fractals in the natural spin-z basis. We present here the details of analytical derivations and numerical confirmations of this statement. PMID:24344342
a New Method for Calculating the Fractal Dimension of Surface Topography
NASA Astrophysics Data System (ADS)
Zuo, Xue; Zhu, Hua; Zhou, Yuankai; Li, Yan
2015-06-01
A new method termed as three-dimensional root-mean-square (3D-RMS) method, is proposed to calculate the fractal dimension (FD) of machined surfaces. The measure of this method is the root-mean-square value of surface data, and the scale is the side length of square in the projection plane. In order to evaluate the calculation accuracy of the proposed method, the isotropic surfaces with deterministic FD are generated based on the fractional Brownian function and Weierstrass-Mandelbrot (WM) fractal function, and two kinds of anisotropic surfaces are generated by stretching or rotating a WM fractal curve. Their FDs are estimated by the proposed method, as well as differential boxing-counting (DBC) method, triangular prism surface area (TPSA) method and variation method (VM). The results show that the 3D-RMS method performs better than the other methods with a lower relative error for both isotropic and anisotropic surfaces, especially for the surfaces with dimensions higher than 2.5, since the relative error between the estimated value and its theoretical value decreases with theoretical FD. Finally, the electrodeposited surface, end-turning surface and grinding surface are chosen as examples to illustrate the application of 3D-RMS method on the real machined surfaces. This method gives a new way to accurately calculate the FD from the surface topographic data.
FRACTAL DIMENSION OF GALAXY ISOPHOTES
Thanki, Sandip; Rhee, George; Lepp, Stephen E-mail: grhee@physics.unlv.edu
2009-09-15
In this paper we investigate the use of the fractal dimension of galaxy isophotes in galaxy classification. We have applied two different methods for determining fractal dimensions to the isophotes of elliptical and spiral galaxies derived from CCD images. We conclude that fractal dimension alone is not a reliable tool but that combined with other parameters in a neural net algorithm the fractal dimension could be of use. In particular, we have used three parameters to segregate the ellipticals and lenticulars from the spiral galaxies in our sample. These three parameters are the correlation fractal dimension D {sub corr}, the difference between the correlation fractal dimension and the capacity fractal dimension D {sub corr} - D {sub cap}, and, thirdly, the B - V color of the galaxy.
Dimension of fractal basin boundaries
Park, B.S.
1988-01-01
In many dynamical systems, multiple attractors coexist for certain parameter ranges. The set of initial conditions that asymptotically approach each attractor is its basin of attraction. These basins can be intertwined on arbitrary small scales. Basin boundary can be either smooth or fractal. Dynamical systems that have fractal basin boundary show final state sensitivity of the initial conditions. A measure of this sensitivity (uncertainty exponent {alpha}) is related to the dimension of the basin boundary d = D - {alpha}, where D is the dimension of the phase space and d is the dimension of the basin boundary. At metamorphosis values of the parameter, there might happen a conversion from smooth to fractal basin boundary (smooth-fractal metamorphosis) or a conversion from fractal to another fractal basin boundary characteristically different from the previous fractal one (fractal-fractal metamorphosis). The dimension changes continuously with the parameter except at the metamorphosis values where the dimension of the basin boundary jumps discontinuously. We chose the Henon map and the forced damped pendulum to investigate this. Scaling of the basin volumes near the metamorphosis values of the parameter is also being studied for the Henon map. Observations are explained analytically by using low dimensional model map.
Exterior dimension of fat fractals
NASA Technical Reports Server (NTRS)
Grebogi, C.; Mcdonald, S. W.; Ott, E.; Yorke, J. A.
1985-01-01
Geometric scaling properties of fat fractal sets (fractals with finite volume) are discussed and characterized via the introduction of a new dimension-like quantity which is called the exterior dimension. In addition, it is shown that the exterior dimension is related to the 'uncertainty exponent' previously used in studies of fractal basin boundaries, and it is shown how this connection can be exploited to determine the exterior dimension. Three illustrative applications are described, two in nonlinear dynamics and one dealing with blood flow in the body. Possible relevance to porous materials and ballistic driven aggregation is also noted.
Box-covering algorithm for fractal dimension of weighted networks.
Wei, Dai-Jun; Liu, Qi; Zhang, Hai-Xin; Hu, Yong; Deng, Yong; Mahadevan, Sankaran
2013-01-01
Box-covering algorithm is a widely used method to measure the fractal dimension of complex networks. Existing researches mainly deal with the fractal dimension of unweighted networks. Here, the classical box covering algorithm is modified to deal with the fractal dimension of weighted networks. Box size length is obtained by accumulating the distance between two nodes connected directly and graph-coloring algorithm is based on the node strength. The proposed method is applied to calculate the fractal dimensions of the "Sierpinski" weighted fractal networks, the E.coli network, the Scientific collaboration network, the C.elegans network and the USAir97 network. Our results show that the proposed method is efficient when dealing with the fractal dimension problem of complex networks. We find that the fractal property is influenced by the edge-weight in weighted networks. The possible variation of fractal dimension due to changes in edge-weights of weighted networks is also discussed. PMID:24157896
Box-covering algorithm for fractal dimension of weighted networks
NASA Astrophysics Data System (ADS)
Wei, Dai-Jun; Liu, Qi; Zhang, Hai-Xin; Hu, Yong; Deng, Yong; Mahadevan, Sankaran
2013-10-01
Box-covering algorithm is a widely used method to measure the fractal dimension of complex networks. Existing researches mainly deal with the fractal dimension of unweighted networks. Here, the classical box covering algorithm is modified to deal with the fractal dimension of weighted networks. Box size length is obtained by accumulating the distance between two nodes connected directly and graph-coloring algorithm is based on the node strength. The proposed method is applied to calculate the fractal dimensions of the ``Sierpinski'' weighted fractal networks, the E.coli network, the Scientific collaboration network, the C.elegans network and the USAir97 network. Our results show that the proposed method is efficient when dealing with the fractal dimension problem of complex networks. We find that the fractal property is influenced by the edge-weight in weighted networks. The possible variation of fractal dimension due to changes in edge-weights of weighted networks is also discussed.
Fractal dimensions of sinkholes
NASA Astrophysics Data System (ADS)
Reams, Max W.
1992-05-01
Sinkhole perimeters are probably fractals ( D=1.209-1.558) for sinkholes with areas larger than 10,000 m 2, based on area-perimeter plots of digitized data from karst surfaces developed on six geologic units in the United States. The sites in Florida, Kentucky, Indiana and Missouri were studied using maps with a scale of 1:24, 000. Size-number distributions of sinkhole perimeters and areas may also be fractal, although data for small sinkholes is needed for verification. Studies based on small-scale maps are needed to evaluate the number and roughness of small sinkhole populations.
Fractal Dimension in Epileptic EEG Signal Analysis
NASA Astrophysics Data System (ADS)
Uthayakumar, R.
Fractal Analysis is the well developed theory in the data analysis of non-linear time series. Especially Fractal Dimension is a powerful mathematical tool for modeling many physical and biological time signals with high complexity and irregularity. Fractal dimension is a suitable tool for analyzing the nonlinear behaviour and state of the many chaotic systems. Particularly in analysis of chaotic time series such as electroencephalograms (EEG), this feature has been used to identify and distinguish specific states of physiological function.Epilepsy is the main fatal neurological disorder in our brain, which is analyzed by the biomedical signal called Electroencephalogram (EEG). The detection of Epileptic seizures in the EEG Signals is an important tool in the diagnosis of epilepsy. So we made an attempt to analyze the EEG in depth for knowing the mystery of human consciousness. EEG has more fluctuations recorded from the human brain due to the spontaneous electrical activity. Hence EEG Signals are represented as Fractal Time Series.The algorithms of fractal dimension methods have weak ability to the estimation of complexity in the irregular graphs. Divider method is widely used to obtain the fractal dimension of curves embedded into a 2-dimensional space. The major problem is choosing initial and final step length of dividers. We propose a new algorithm based on the size measure relationship (SMR) method, quantifying the dimensional behaviour of irregular rectifiable graphs with minimum time complexity. The evidence for the suitability (equality with the nature of dimension) of the algorithm is illustrated graphically.We would like to demonstrate the criterion for the selection of dividers (minimum and maximum value) in the calculation of fractal dimension of the irregular curves with minimum time complexity. For that we design a new method of computing fractal dimension (FD) of biomedical waveforms. Compared to Higuchi's algorithm, advantages of this method include
Nieckarz, Zenon; Tatoń, Grzegorz; Kozerska, Magdalena; Skrzat, Janusz; Sioma, Andrzej
2015-01-01
We presented a novel approach to studies of the vascular grooves located on the inner surface of the cranial vault. A three-dimensional vision system that acquired the endocranial surface topography was used for this purpose. The acquired data were used to generate images showing the branching pattern of the middle meningeal artery. Fractal dimension was used to characterize and analyze branching pattern complexity. We discussed the usefulness of the latter method and indicated difficulties and potential errors connected to the fractal dimension application. The technique introduced for recording traits of the object surface appears to be helpful in anatomical study of morphological variation of dural vascularization. It may also be applicable in paleoneurological research based on analysis of the cranial remnants. Fractal dimension should be used carefully as a method sensitive to many aspects of data acquisition and processing. PMID:25807002
Fractal dimension of bioconvection patterns
NASA Technical Reports Server (NTRS)
Noever, David A.
1990-01-01
Shallow cultures of the motile algal strain, Euglena gracilis, were concentrated to 2 x 10 to the 6th organisms per ml and placed in constant temperature water baths at 24 and 38 C. Bioconvective patterns formed an open two-dimensional structure with random branches, similar to clusters encountered in the diffusion-limited aggregation (DLA) model. When averaged over several example cultures, the pattern was found to have no natural length scale, self-similar branching, and a fractal dimension (d about 1.7). These agree well with the two-dimensional DLA.
Fractal Dimension of Bioconvection Patterns
NASA Astrophysics Data System (ADS)
Noever, David A.
1990-10-01
Shallow cultures of the motile algal strain, Euglena gracilis, were concentrated to 2× 106 organisms per ml and placed in constant temperature water baths at 24 and 38 C. Bioconvective patterns formed an open two-dimensional structure with random branches, similar to clusters encountered in the diffusion-limited aggregation (DLA) model. When averaged over several example cultures, the pattern was found to have no natural length scale, self-similar branching and a fractal dimension (d˜1.7). These agree well with the two-dimensional DLA.
A Fractal Dimension Survey of Active Region Complexity
NASA Technical Reports Server (NTRS)
McAteer, R. T. James; Gallagher, Peter; Ireland, Jack
2005-01-01
A new approach to quantifying the magnetic complexity of active regions using a fractal dimension measure is presented. This fully-automated approach uses full disc MDI magnetograms of active regions from a large data set (2742 days of the SoHO mission; 9342 active regions) to compare the calculated fractal dimension to both Mount Wilson classification and flare rate. The main Mount Wilson classes exhibit no distinct fractal dimension distribution, suggesting a self-similar nature of all active regions. Solar flare productivity exhibits an increase in both the frequency and GOES X-ray magnitude of flares from regions with higher fractal dimensions. Specifically a lower threshold fractal dimension of 1.2 and 1.25 exists as a necessary, but not sufficient, requirement for an active region to produce M- and X-class flares respectively .
Fractal Dimensions of Macromolecular Structures
Todoroff, Nickolay; Kunze, Jens; Schreuder, Herman; Hessler, Gerhard; Baringhaus, Karl-Heinz; Schneider, Gisbert
2014-01-01
Quantifying the properties of macromolecules is a prerequisite for understanding their roles in biochemical processes. One of the less-explored geometric features of macromolecules is molecular surface irregularity, or ‘roughness’, which can be measured in terms of fractal dimension (D). In this study, we demonstrate that surface roughness correlates with ligand binding potential. We quantified the surface roughnesses of biological macromolecules in a large-scale survey that revealed D values between 2.0 and 2.4. The results of our study imply that surface patches involved in molecular interactions, such as ligand-binding pockets and protein-protein interfaces, exhibit greater local fluctuations in their fractal dimensions than ‘inert’ surface areas. We expect approximately 22 % of a protein’s surface outside of the crystallographically known ligand binding sites to be ligandable. These findings provide a fresh perspective on macromolecular structure and have considerable implications for drug design as well as chemical and systems biology. PMID:26213587
NASA Astrophysics Data System (ADS)
Yan, Kun
2007-04-01
In this paper, by discussing the basic hypotheses about the continuous orbit and discrete orbit in two research directions of the background medium theory for celestial body motion, the concrete equation forms and their summary of the theoretic frame of celestial body motion are introduced. Future more, by discussing the general form of Binet's equation of celestial body motion orbit and it's solution of the advance of the perihelion of planets, the relations and differences between the continuous orbit theory and Newton's gravitation theory and Einstein's general relativity are given. And by discussing the fractional-dimension expanded equation for the celestial body motion orbits, the concrete equations and the prophesy data of discrete orbit or stable orbits of celestial bodies which included the planets in the Solar system, satellites in the Uranian system, satellites in the Earth system and satellites obtaining the Moon obtaining from discrete orbit theory are given too. Especially, as the preliminary exploration and inference to the gravitation curve of celestial bodies in broadly range, the concept for the ideal black hole with trend to infinite in mass density difficult to be formed by gravitation only is explored. By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying
Dimension of a fractal streamer structure
NASA Astrophysics Data System (ADS)
Lehtinen, Nikolai G.; Østgaard, Nikolai
2015-04-01
Streamer corona plays an important role in formation of leader steps in lightning. In order to understand its dynamics, the streamer front velocity is calculated in a 1D model with curvature. We concentrate on the role of photoionization mechanism in the propagation of the streamer ionization front, the other important mechanisms being electron drift and electron diffusion. The results indicate, in particular, that the effect of photoionization on the streamer velocity for both positive and negative streamers is mostly determined by the photoionization length, with a weaker dependence on the amount of photoionization, and that the velocity is decreased for positive curvature, i.e., convex fronts. These results are used in a fractal model in which the front propagation velocity is simulated as the cluster growth probability [Niemeyer et al, 1984, doi:10.1103/PhysRevLett.52.1033]. Monte Carlo simulations of the cluster growth for various ratios of background electric field E to the breakdown field Eb show that the emerging transverse size of the streamers is of the order of the photoionization length, and at the larger scale the streamer structure is a fractal similar to the one obtained in a diffusion-limited aggregation (DLA) system. In the absence of electron attachment (Eb = 0), the fractal dimension is the same (D ˜ 1.67) as in the DLA model, and is reduced, i.e., the fractal has less branching, for Eb > 0.
Fractal dimension of cerebral surfaces using magnetic resonance images
Majumdar, S.; Prasad, R.R.
1988-11-01
The calculation of the fractal dimension of the surface bounded by the grey matter in the normal human brain using axial, sagittal, and coronal cross-sectional magnetic resonance (MR) images is presented. The fractal dimension in this case is a measure of the convolutedness of this cerebral surface. It is proposed that the fractal dimension, a feature that may be extracted from MR images, may potentially be used for image analysis, quantitative tissue characterization, and as a feature to monitor and identify cerebral abnormalities and developmental changes.
Randomness in fractals, connectivity dimensions, and percolation
NASA Astrophysics Data System (ADS)
Perreau, M.; Levy, J. C. S.
1989-10-01
The structural properties of random fractals embedded in a d-dimensional Euclidean space are studied by means of transfer-matrix formalism of fractal sets. For d=1, both global and local approaches have been investigated, leading to the definition of a subdimension that is different from the fractal dimension and depends on the probability distribution. This subdimension is shown to be identical for the global and local approaches; then, the scaling corrections involved in this subdimension are the same for both these approaches. For d>1, only the local approach can be generalized, characterizing the connectivity properties of these structures. There are exactly d subdimensions called connectivity dimensions that prove to be useful to describe percolation properties of these fractals. Several percolation thresholds are shown, and the fractal dimension of the sets at the percolation threshold are related to the connectivity dimensions.
The use of fractal dimension for texture classification
Dixon, K.E.
1989-04-01
This paper addresses the idea of using fractal dimension as a measure of image texture. The computation of the fractal dimension of a grey-scale image and also of the ''fractal signature'' of the image is presented. Two methods of scanning the image for these calculations are introduced: a line scan and a window scan. Several subsets of features extracted from the calculations are investigated as features for classification of the texture. Results from various classification experiments are presented. 5 refs., 8 tabs.
Trabecular Bone Mechanical Properties and Fractal Dimension
NASA Technical Reports Server (NTRS)
Hogan, Harry A.
1996-01-01
Countermeasures for reducing bone loss and muscle atrophy due to extended exposure to the microgravity environment of space are continuing to be developed and improved. An important component of this effort is finite element modeling of the lower extremity and spinal column. These models will permit analysis and evaluation specific to each individual and thereby provide more efficient and effective exercise protocols. Inflight countermeasures and post-flight rehabilitation can then be customized and targeted on a case-by-case basis. Recent Summer Faculty Fellowship participants have focused upon finite element mesh generation, muscle force estimation, and fractal calculations of trabecular bone microstructure. Methods have been developed for generating the three-dimensional geometry of the femur from serial section magnetic resonance images (MRI). The use of MRI as an imaging modality avoids excessive exposure to radiation associated with X-ray based methods. These images can also detect trabecular bone microstructure and architecture. The goal of the current research is to determine the degree to which the fractal dimension of trabecular architecture can be used to predict the mechanical properties of trabecular bone tissue. The elastic modulus and the ultimate strength (or strain) can then be estimated from non-invasive, non-radiating imaging and incorporated into the finite element models to more accurately represent the bone tissue of each individual of interest. Trabecular bone specimens from the proximal tibia are being studied in this first phase of the work. Detailed protocols and procedures have been developed for carrying test specimens through all of the steps of a multi-faceted test program. The test program begins with MRI and X-ray imaging of the whole bones before excising a smaller workpiece from the proximal tibia region. High resolution MRI scans are then made and the piece further cut into slabs (roughly 1 cm thick). The slabs are X-rayed again
Edge extraction of optical subaperture based on fractal dimension method
NASA Astrophysics Data System (ADS)
Wang, Yunqi; Hui, Mei; Liu, Ming; Dong, Liquan; Liu, Xiaohua; Zhao, Yuejin
2015-09-01
Optical synthetic aperture imaging technology is an effective approach to increase the aperture diameter of optical system for purpose of improving resolution. In optical synthetic aperture imaging system, the edge is more complex than that of traditional optical imaging system, and the relatively large size of the gaps between the subapertures makes cophasing a difficult problem. So it is significant to extract edge phase of each subaperture for achieving phase stitching and avoiding the loss of effective frequency. Fractal dimension as a measure feature of image surface irregularities can statistically evaluate the complexity which is consistent with human visual image perception of rough surface texture. Therefore, fractal dimension provides a powerful tool to describe surface characteristics of image and can be applied to edge extraction. In our research, the box-counting dimension was used to calculate fractal dimension of the whole image. Then the calculated fractal dimension is mapped to grayscale image. The region with large fractal dimension represents a sharper change of the gray scale in original image, which was accurately extracted as the edge region. Subaperture region and interference fringe edge was extracted from interference pattern of optical subaperture, which has laid the foundation for the subaperture edge phase detection in the future work.
Fractal Dimensions and Entropies of Meragi Songs
NASA Astrophysics Data System (ADS)
Aydemir, Adnan; Gündüz, Güngör
Melodies can be treated as time series
Fractal dimension of microbead assemblies used for protein detection
Hecht, Ariel; Commiskey, Patrick; Lazaridis, Filippos; Argyrakis, Panos
2014-01-01
We use fractal analysis to calculate the protein concentration in a rotating magnetic assembly of microbeads of size 1μm, which has optimized parameters of sedimentation, binding sites and magnetic volume. We utilize the original Forrest-Witten method, but due to the relatively small number of bead particles, which is of the order of 500, we use a large number of origins and also a large number of algorithm iterations. We find a value of the fractal dimension in the range 1.70–1.90, as a function of the thrombin concentration, which plays the role of binding the microbeads together. This is in good agreement with previous results from magnetorotation studies. The calculation of the fractal dimension using multiple points of reference can be used for any assembly with a relatively small number of particles. PMID:25195559
ERIC Educational Resources Information Center
Esbenshade, Donald H., Jr.
1991-01-01
Develops the idea of fractals through a laboratory activity that calculates the fractal dimension of ordinary white bread. Extends use of the fractal dimension to compare other complex structures as other breads and sponges. (MDH)
The Correlation Fractal Dimension of Complex Networks
NASA Astrophysics Data System (ADS)
Wang, Xingyuan; Liu, Zhenzhen; Wang, Mogei
2013-05-01
The fractality of complex networks is studied by estimating the correlation dimensions of the networks. Comparing with the previous algorithms of estimating the box dimension, our algorithm achieves a significant reduction in time complexity. For four benchmark cases tested, that is, the Escherichia coli (E. Coli) metabolic network, the Homo sapiens protein interaction network (H. Sapiens PIN), the Saccharomyces cerevisiae protein interaction network (S. Cerevisiae PIN) and the World Wide Web (WWW), experiments are provided to demonstrate the validity of our algorithm.
Fractal dimension of alumina aggregates grown in two dimensions
NASA Technical Reports Server (NTRS)
Larosa, Judith L.; Cawley, James D.
1992-01-01
The concepts of fractal geometry are applied to the analysis of 0.4-micron alumina constrained to agglomerate in two dimensions. Particles were trapped at the bottom surface of a drop of a dilute suspension, and the agglomeration process was directly observed, using an inverted optical microscope. Photographs were digitized and analyzed, using three distinct approaches. The results indicate that the agglomerates are fractal, having a dimension of approximately 1.5, which agrees well with the predictions of the diffusion-limited cluster-cluster aggregation model.
Estimation of fractal dimensions from transect data
Loehle, C.
1994-04-01
Fractals are a useful tool for analyzing the topology of objects such as coral reefs, forest canopies, and landscapes. Transects are often studied in these contexts, and fractal dimensions computed from them. An open question is how representative a single transect is. Transects may also be used to estimate the dimensionality of a surface. Again the question of representativeness of the transect arises. These two issues are related. This note qualifies the conditions under which transect data may be considered to be representative or may be extrapolated, based on both theoretical and empirical results.
Design and application of quick computation program on fractal dimension of land-use types
NASA Astrophysics Data System (ADS)
Mei, Xin; Wang, Quanfang; Wang, Qian; Liu, Junyi
2009-07-01
Now the fractal dimension of Land Use Types is often calculated by using raster data as the raw data, but quite a number of spatial data is stored as vector data in fact. If these data are converted to images to calculate fractal dimension, perhaps some pixels with inaccurate grey value will result from the "GRID" structure of raster data. And the precision of fractal dimension calculated on raster Data is closely related to the size of pixel and Grid image.In view of this, In this paper, a computation program of the fractal dimension for 2D vector data based on Windows platform has been designed by using Visual Csharp. This program has been successfully applied to land-use data of the middle Qinling Mountains and the southeast of Hubei Province in China.in the 1990s. The results show that the program is a convenient, reliable and precise method of fractal dimension for 2D Vector Data.
Fractal dimension analyses of lava surfaces and flow boundaries
NASA Technical Reports Server (NTRS)
Cleghorn, Timothy F.
1993-01-01
An improved method of estimating fractal surface dimensions has been developed. The accuracy of this method is illustrated using artificially generated fractal surfaces. A slightly different from usual concept of linear dimension is developed, allowing a direct link between that and the corresponding surface dimension estimate. These methods are applied to a series of images of lava flows, representing a variety of physical and chemical conditions. These include lavas from California, Idaho, and Hawaii, as well as some extraterrestrial flows. The fractal surface dimension estimations are presented, as well as the fractal line dimensions where appropriate.
Local Earth's gravity field in view of fractal dimension
NASA Astrophysics Data System (ADS)
Mészárosová, Katarína; Minarechová, Zuzana; Janák, Juraj
2013-04-01
The poster presents the relative roughness of chosen characteristics of the Earth's gravity field in several small regions in area of Slovakia (e.g. free-air anomaly, Bouguer anomaly, gravity disturbance...) using the values of fractal dimension. In this approach, a three dimensional box counting method and the Hurst analysis method are applied to estimate the values of fractal dimensions. Then the computed fractal dimension values are used to compare all 3D models of all chosen characteristics.
Fractal dimension in nonhyperbolic chaotic scattering
NASA Technical Reports Server (NTRS)
Lau, Yun-Tung; Finn, John M.; Ott, Edward
1991-01-01
In chaotic scattering there is a Cantor set of input-variable values of zero Lebesgue measure (i.e., zero total length) on which the scattering function is singular. For cases where the dynamics leading to chaotic scattering is nonhyperbolic (e.g., there are Kolmogorov-Arnol'd-Moser tori), the nature of this singular set is fundamentally different from that in the hyperbolic case. In particular, for the nonhyperbolic case, although the singular set has zero total length, strong evidence is presented to show that its fractal dimension is 1.
Fractal dimension based corneal fungal infection diagnosis
NASA Astrophysics Data System (ADS)
Balasubramanian, Madhusudhanan; Perkins, A. Louise; Beuerman, Roger W.; Iyengar, S. Sitharama
2006-08-01
We present a fractal measure based pattern classification algorithm for automatic feature extraction and identification of fungus associated with an infection of the cornea of the eye. A white-light confocal microscope image of suspected fungus exhibited locally linear and branching structures. The pixel intensity variation across the width of a fungal element was gaussian. Linear features were extracted using a set of 2D directional matched gaussian-filters. Portions of fungus profiles that were not in the same focal plane appeared relatively blurred. We use gaussian filters of standard deviation slightly larger than the width of a fungus to reduce discontinuities. Cell nuclei of cornea and nerves also exhibited locally linear structure. Cell nuclei were excluded by their relatively shorter lengths. Nerves in the cornea exhibited less branching compared with the fungus. Fractal dimensions of the locally linear features were computed using a box-counting method. A set of corneal images with fungal infection was used to generate class-conditional fractal measure distributions of fungus and nerves. The a priori class-conditional densities were built using an adaptive-mixtures method to reflect the true nature of the feature distributions and improve the classification accuracy. A maximum-likelihood classifier was used to classify the linear features extracted from test corneal images as 'normal' or 'with fungal infiltrates', using the a priori fractal measure distributions. We demonstrate the algorithm on the corneal images with culture-positive fungal infiltrates. The algorithm is fully automatic and will help diagnose fungal keratitis by generating a diagnostic mask of locations of the fungal infiltrates.
Single cell correlation fractal dimension of chromatin
Récamier, Vincent; Izeddin, Ignacio; Bosanac, Lana; Dahan, Maxime; Proux, Florence; Darzacq, Xavier
2014-01-01
Chromatin is a major nuclear component, and it is an active matter of debate to understand its different levels of spatial organization, as well as its implication in gene regulation. Measurements of nuclear chromatin compaction were recently used to understand how DNA is folded inside the nucleus and to detect cellular dysfunctions such as cancer. Super-resolution imaging opens new possibilities to measure chromatin organization in situ. Here, we performed a direct measure of chromatin compaction at the single cell level. We used histone H2B, one of the 4 core histone proteins forming the nucleosome, as a chromatin density marker. Using photoactivation localization microscopy (PALM) and adaptive optics, we measured the three-dimensional distribution of H2B with nanometric resolution. We computed the distribution of distances between every two points of the chromatin structure, namely the Ripley K(r) distribution. We found that the K(r) distribution of H2B followed a power law, leading to a precise measurement of the correlation fractal dimension of chromatin of 2.7. Moreover, using photoactivable GFP fused to H2B, we observed dynamic evolution of chromatin sub-regions compaction. As a result, the correlation fractal dimension of chromatin reported here can be interpreted as a dynamically maintained non-equilibrium state. PMID:24637833
Vahedi, Arman; Gorczyca, Beata
2012-09-01
Here we introduce a distribution of floc fractal dimensions as opposed to a single fractal dimension value into the floc settling velocity model developed in earlier studies. The distribution of fractal dimensions for a single floc size was assumed to cover a range from 1.9 to 3.0. This range was selected based on the theoretically determined fractal dimensions for diffusion-limited and cluster-cluster aggregation. These two aggregation mechanisms are involved in the formation of the lime softening flocs analyzed in this study. Fractal dimensions were generated under the assumption that a floc can have any value of normally distributed fractal dimensions ranging from 1.9-3.0. A range of settling velocities for a single floc size was calculated based on the distribution of fractal dimensions. The assumption of multiple fractal dimensions for a single floc size resulted in a non-unique relationship between the floc size and the floc settling velocity, i.e., several different settling velocities were calculated for one floc size. The settling velocities calculated according to the model ranged from 0 to 10 mm/s (average 2.22 mm/s) for the majority of flocs in the size range of 1-250 μm (average 125 μm). The experimentally measured settling velocities of flocs ranged from 0.1 to 7.1 mm/s (average 2.37 mm/s) for the flocs with equivalent diameters from 10 μm to 260 μm (average 124 μm). Experimentally determined floc settling velocities were predicted well by the floc settling model incorporating distributions of floc fractal dimensions calculated based on the knowledge of the mechanisms of aggregation, i.e., cluster-cluster aggregation and diffusion-limited aggregation. PMID:22673348
Fractal Dimension in Eeg Signals during Muscle Fatigue
NASA Astrophysics Data System (ADS)
Huang, Haibin; Yao, Bin; Yue, Guang; Brown, Robert; Jing, Liu
2003-10-01
Fractal dimension (FD) has been successfully used to characterize signals in the format of time series. In this study, we calculated FD of EEG signals recorded during human muscle fatigue as a measure of changes in the EEG signal complexity along fatigue. Subjects performed 200 intermittent handgrip contractions at 100contraction level. Each contraction lasted 2 s, followed by a 5-s rest. EEG data were recorded from the scalp along with handgrip force and muscle EMG signals. The FD computation was based on measurements of the length (Lk) of the signal at 6 different temporal resolutions (k = 1, 2, ¡, 6). FD was determined from the relationship between Lk and k using the least square fit. The results showed that: (1) EEG fractal dimension associated with the motor performance was significantly higher than that during the rest period; (2) changes in the fractal dimension along the process of fatigue showed a significant correlation with the decline in force and EMG signals.
Pyramidal fractal dimension for high resolution images
NASA Astrophysics Data System (ADS)
Mayrhofer-Reinhartshuber, Michael; Ahammer, Helmut
2016-07-01
Fractal analysis (FA) should be able to yield reliable and fast results for high-resolution digital images to be applicable in fields that require immediate outcomes. Triggered by an efficient implementation of FA for binary images, we present three new approaches for fractal dimension (D) estimation of images that utilize image pyramids, namely, the pyramid triangular prism, the pyramid gradient, and the pyramid differences method (PTPM, PGM, PDM). We evaluated the performance of the three new and five standard techniques when applied to images with sizes up to 8192 × 8192 pixels. By using artificial fractal images created by three different generator models as ground truth, we determined the scale ranges with minimum deviations between estimation and theory. All pyramidal methods (PM) resulted in reasonable D values for images of all generator models. Especially, for images with sizes ≥1024 ×1024 pixels, the PMs are superior to the investigated standard approaches in terms of accuracy and computation time. A measure for the possibility to differentiate images with different intrinsic D values did show not only that the PMs are well suited for all investigated image sizes, and preferable to standard methods especially for larger images, but also that results of standard D estimation techniques are strongly influenced by the image size. Fastest results were obtained with the PDM and PGM, followed by the PTPM. In terms of absolute D values best performing standard methods were magnitudes slower than the PMs. Concluding, the new PMs yield high quality results in short computation times and are therefore eligible methods for fast FA of high-resolution images.
Pyramidal fractal dimension for high resolution images.
Mayrhofer-Reinhartshuber, Michael; Ahammer, Helmut
2016-07-01
Fractal analysis (FA) should be able to yield reliable and fast results for high-resolution digital images to be applicable in fields that require immediate outcomes. Triggered by an efficient implementation of FA for binary images, we present three new approaches for fractal dimension (D) estimation of images that utilize image pyramids, namely, the pyramid triangular prism, the pyramid gradient, and the pyramid differences method (PTPM, PGM, PDM). We evaluated the performance of the three new and five standard techniques when applied to images with sizes up to 8192 × 8192 pixels. By using artificial fractal images created by three different generator models as ground truth, we determined the scale ranges with minimum deviations between estimation and theory. All pyramidal methods (PM) resulted in reasonable D values for images of all generator models. Especially, for images with sizes ≥1024×1024 pixels, the PMs are superior to the investigated standard approaches in terms of accuracy and computation time. A measure for the possibility to differentiate images with different intrinsic D values did show not only that the PMs are well suited for all investigated image sizes, and preferable to standard methods especially for larger images, but also that results of standard D estimation techniques are strongly influenced by the image size. Fastest results were obtained with the PDM and PGM, followed by the PTPM. In terms of absolute D values best performing standard methods were magnitudes slower than the PMs. Concluding, the new PMs yield high quality results in short computation times and are therefore eligible methods for fast FA of high-resolution images. PMID:27475069
Estimating fractal dimension of medical images
NASA Astrophysics Data System (ADS)
Penn, Alan I.; Loew, Murray H.
1996-04-01
Box counting (BC) is widely used to estimate the fractal dimension (fd) of medical images on the basis of a finite set of pixel data. The fd is then used as a feature to discriminate between healthy and unhealthy conditions. We show that BC is ineffective when used on small data sets and give examples of published studies in which researchers have obtained contradictory and flawed results by using BC to estimate the fd of data-limited medical images. We present a new method for estimating fd of data-limited medical images. In the new method, fractal interpolation functions (FIFs) are used to generate self-affine models of the underlying image; each model, upon discretization, approximates the original data points. The fd of each FIF is analytically evaluated. The mean of the fds of the FIFs is the estimate of the fd of the original data. The standard deviation of the fds of the FIFs is a confidence measure of the estimate. The goodness-of-fit of the discretized models to the original data is a measure of self-affinity of the original data. In a test case, the new method generated a stable estimate of fd of a rib edge in a standard chest x-ray; box counting failed to generate a meaningful estimate of the same image.
Fractal dimension analysis of complexity in Ligeti piano pieces
NASA Astrophysics Data System (ADS)
Bader, Rolf
2005-04-01
Fractal correlation dimensional analysis has been performed with whole solo piano pieces by Gyrgy Ligeti at every 50ms interval of the pieces. The resulting curves of development of complexity represented by the fractal dimension showed up a very reasonable correlation with the perceptional density of events during these pieces. The seventh piece of Ligeti's ``Musica ricercata'' was used as a test case. Here, each new part of the piece was followed by an increase of the fractal dimension because of the increase of information at the part changes. The second piece ``Galamb borong,'' number seven of the piano Etudes was used, because Ligeti wrote these Etudes after studying fractal geometry. Although the piece is not fractal in the strict mathematical sense, the overall structure of the psychoacoustic event-density as well as the detailed event development is represented by the fractal dimension plot.
Fractal dimension and mechanism of aggregation of apple juice particles.
Benítez, E I; Lozano, J E; Genovese, D B
2010-04-01
Turbidity of freshly squeezed apple juice is produced by a polydisperse suspension of particles coming from the cellular tissue. After precipitation of coarse particles by gravity, only fine-colloidal particles remain in suspension. Aggregation of colloidal particles leads to the formation of fractal structures. The fractal dimension is a measure of the internal density of these aggregates and depends on their mechanism of aggregation. Digitized images of primary particles and aggregates of depectinized, diafiltered cloudy apple juice were obtained by scanning electron microscopy (SEM). Average radius of the primary particles was found to be a = 40 ± 11 nm. Maximum radius of the aggregates, R(L), ranged between 250 and 7750 nm. Fractal dimension of the aggregates was determined by analyzing SEM images with the variogram method, obtaining an average value of D(f) = 2.3 ± 0.1. This value is typical of aggregates formed by rapid flocculation or diffusion limited aggregation. Diafiltration process was found to reduce the average size and polydispersity of the aggregates, determined by photon correlation spectroscopy. Average gyration radius of the aggregates before juice diafiltration was found to be R(g) = 629 ± 87 nm. Average number of primary particles per aggregate was calculated to be N = 1174. PMID:21339133
Heterogeneities Analysis Using the Generalized Fractal Dimension and Continuous Wavelet Transform
NASA Astrophysics Data System (ADS)
Ouadfeul, S.; Aliouane, L.; Boudella, A.
2012-04-01
The main goal of this work is analyze heterogeneities from well-logs data using the wavelet transform modulus maxima lines (WTMM). Firstly, the continuous wavelet transform (CWT) with sliding window is calculated. The next step consists to calculate the maxima of the modulus of the CWT and estimate the spectrum of exponents. The three generalized fractal dimensions D0, D1 and D2 are then estimated. Application of the proposed idea at the synthetic and real well-logs data of a borehole located in the Algerian Sahara shows that the fractal dimensions are very sensitive to lithological variations. The generalized fractal dimensions are a very robust tool than can be used for petroleum reservoir characterization. Keywrods: reservoir, Heterogeneities, WTMM, fractal dimension.
Surface fractal dimension of sintered porous solid niobium
NASA Astrophysics Data System (ADS)
Skatkov, L. I.; Konotop, V. V.; Cheremskoy, P. G.; Gomozov, V. P.; Bayrachny, B. I.
1994-12-01
The surface fractal dimension of porous solid niobium obtained by vacuum sintering Nb powder is experimentally investigated. The surface fractal dimension D is the main object of our study. Results of small-angle X-ray scattering (SAXS) agree very closely with those of Hg porosimetry. The surface dimensions are stated to be of the order of 2.8 which is a stipulation of a highly developed porous structure. Our results provide experimental support to the SAXS theory developed earlier.
NASA Astrophysics Data System (ADS)
Ulyanov, Alexander S.; Lyapina, Anna M.; Ulianova, Onega V.; Feodorova, Valentina A.
2010-10-01
New field of application of fractal dimensions is proposed. A technique, based on the calculation of fractal dimension, was used for express-diagnostics and identification of bacteria of the vaccine strain Yersinia pestis EV line NIIEG. Purpose of this study was the experimental investigation of properties of speckle patterns, formed under laser illumination of a single colony of the strain that was grown on different agars.
NASA Astrophysics Data System (ADS)
Ulyanov, Alexander S.; Lyapina, Anna M.; Ulianova, Onega V.; Feodorova, Valentina A.
2011-03-01
New field of application of fractal dimensions is proposed. A technique, based on the calculation of fractal dimension, was used for express-diagnostics and identification of bacteria of the vaccine strain Yersinia pestis EV line NIIEG. Purpose of this study was the experimental investigation of properties of speckle patterns, formed under laser illumination of a single colony of the strain that was grown on different agars.
FRACTAL DIMENSION RESULTS FOR CONTINUOUS TIME RANDOM WALKS
Meerschaert, Mark M.; Nane, Erkan; Xiao, Yimin
2013-01-01
Continuous time random walks impose random waiting times between particle jumps. This paper computes the fractal dimensions of their process limits, which represent particle traces in anomalous diffusion. PMID:23482421
Archaeon and archaeal virus diversity classification via sequence entropy and fractal dimension
NASA Astrophysics Data System (ADS)
Tremberger, George, Jr.; Gallardo, Victor; Espinoza, Carola; Holden, Todd; Gadura, N.; Cheung, E.; Schneider, P.; Lieberman, D.; Cheung, T.
2010-09-01
Archaea are important potential candidates in astrobiology as their metabolism includes solar, inorganic and organic energy sources. Archaeal viruses would also be expected to be present in a sustainable archaeal exobiological community. Genetic sequence Shannon entropy and fractal dimension can be used to establish a two-dimensional measure for classification and phylogenetic study of these organisms. A sequence fractal dimension can be calculated from a numerical series consisting of the atomic numbers of each nucleotide. Archaeal 16S and 23S ribosomal RNA sequences were studied. Outliers in the 16S rRNA fractal dimension and entropy plot were found to be halophilic archaea. Positive correlation (R-square ~ 0.75, N = 18) was observed between fractal dimension and entropy across the studied species. The 16S ribosomal RNA sequence entropy correlates with the 23S ribosomal RNA sequence entropy across species with R-square 0.93, N = 18. Entropy values correspond positively with branch lengths of a published phylogeny. The studied archaeal virus sequences have high fractal dimensions of 2.02 or more. A comparison of selected extremophile sequences with archaeal sequences from the Humboldt Marine Ecosystem database (Wood-Hull Oceanography Institute, MIT) suggests the presence of continuous sequence expression as inferred from distributions of entropy and fractal dimension, consistent with the diversity expected in an exobiological archaeal community.
Multiorder boundaries among discrete domains: relative fractal dimension and others.
Xuan, Qi; Du, Fang; Wu, Tie-Jun
2010-03-01
In nature and society, most of competitions take place on the boundaries among a group of domains where different individuals or colonies share common resources; therefore, it is widely believed that domain boundaries play important roles in the evolution of many complex systems. Here, we first give a definition for multiorder boundaries among discrete domains and then propose a general method to calculate their relative fractal dimension, i.e., the ratio of the fractal dimension of the boundaries versus that of the domains themselves. Through analyzing three types of real-world discrete domains, several interesting results are revealed. For example, the limitation on the number of domains that an individual can join in may produce longer boundaries indicating more cruel competitions among the domains. Besides, the individuals with more social links are always considered more important in social networks, and it is found that these individuals as valuable resources of social domains are always centralized on the boundaries of higher order. PMID:20370288
Fractal dimension and unscreened angles measured for radial viscous fingering.
Praud, Olivier; Swinney, Harry L
2005-07-01
We have examined fractal patterns formed by the injection of air into oil in a thin (0.127 mm) layer contained between two cylindrical glass plates of 288 mm diameter (a Hele-Shaw cell), for pressure differences in the range 0.25 < or = DeltaP < or = 1.75 atm. We find that an asymptotic structure is reached at large values of the ratio r/b, where r is the pattern radius and b the gap between the plates. Both the driving force and the size of the pattern, which reaches r/b = 900, are far larger than in past experiments. The fractal dimension D0 of the pattern for large r/b is 1.70 +/- 0.02. Further, the generalized dimensions D(q) of the pattern are independent of q , D(q) approximately 1.70 for the range examined, -11 < q < 17; thus the pattern is self-similar within the experimental uncertainty. The results for D(q) agree well with recent calculations for diffusion-limited aggregation (DLA) clusters. We have also measured the probability distribution of unscreened angles. At late times, the distribution approaches a universal (i.e., forcing and size-independent) asymptotic form that has mean 145 degrees Celsius and standard deviation 36 degrees Celsius. These results indicate that the distribution function for the unscreened angle is an invariant property of the growth process. PMID:16089960
Fractal dimensions of rampart impact craters on Mars
NASA Technical Reports Server (NTRS)
Ching, Delwyn; Taylor, G. Jeffrey; Mouginis-Mark, Peter; Bruno, Barbara C.
1993-01-01
Ejecta blanket morphologies of Martian rampart craters may yield important clues to the atmospheric densities during impact, and the nature of target materials (e.g., hard rock, fine-grained sediments, presence of volatiles). In general, the morphologies of such craters suggest emplacement by a fluidized, ground hugging flow instead of ballistic emplacement by dry ejecta. We have quantitatively characterized the shape of the margins of the ejecta blankets of 15 rampart craters using fractal geometry. Our preliminary results suggest that the craters are fractals and are self-similar over scales of approximately 0.1 km to 30 km. Fractal dimensions (a measure of the extent to which a line fills a plane) range from 1.06 to 1.31. No correlations of fractal dimension with target type, elevation, or crater size were observed, though the data base is small. The range in fractal dimension and lack of correlation may be due to a complex interplay of target properties (grain size, volatile content), atmospheric pressure, and crater size. The mere fact that the ejecta margins are fractals, however, indicates that viscosity and yield strength of the ejecta were at least as low as those of basalts, because silicic lava flows are not generally fractals.
Relationship between the fractal dimension and the width to length ratio of mass movements
NASA Astrophysics Data System (ADS)
Sezer, Ebru
2009-04-01
Mass movements have some typical geometrical dimensions. One of these typical geometrical dimensions is the width to length ratio. Also, the fractal dimensions of mass movements from the inventory maps of natural mass movements can be used for their geometrical description and characterization. For this reason, in the present study, development of a computer programme for digitizing and determining the fractal dimensions of mass movements, and investigation of the relationship between the fractal dimensions and the width to length (W/L) tario of the mass movements are aimed. For the purpose of the study, a computer programme namely FRACEK for determination of fractal dimensions of amorphous areas is developed by using the JAVA computer language at first. Secondly, a database including the shapes of the mass movements was compiled from the literature and digitized. Then, their width to length ratios and fractal dimensions were calculated. Finally, a series of simple statistical analyses were performed on the data obtained and the results were interpreted. To investigate the relationships between the fractal dimensions and W/L ratios of the mass movements, a series of simple regression analysis is performed. During the regression analyses, linear, power, logarithmic and exponential functions are employed. According to the results obtained, there are some correlations between the D and the W/L ratio. When considering only debris flow data, a power relationship between the D and the W/L ratio was found and its coefficient of correlation was obtained as 0.85. The lowest coefficient of correlations were obtained from the rotational failure data. The coefficients of correlations of the power and exponential funtions were same, 0.53. A similar result was obtained for the translational failure data. Their coefficient of correlations was 0.74. When all data is evaluated together, a relatively strong correlation between the D and the W/L ratio was obtained. These results
NASA Astrophysics Data System (ADS)
Gao, Wei; Zakharov, Valery P.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Artemyev, Dmitry N.; Kornilin, Dmitry V.
2015-07-01
Optical coherence tomography (OCT) is usually employed for the measurement of retinal thickness characterizing the structural changes of tissue. However, fractal dimension (FD) could also character the structural changes of tissue. Therefore, fractal dimension changes may provide further information regarding cellular layers and early damage in ocular diseases. We investigated the possibility of OCT in detecting changes in fractal dimension from layered retinal structures. OCT images were obtained from diabetic patients without retinopathy (DM, n = 38 eyes) or mild diabetic retinopathy (MDR, n = 43 eyes) and normal healthy subjects (Controls, n = 74 eyes). Fractal dimension was calculated using the differentiate box counting methodology. We evaluated the usefulness of quantifying fractal dimension of layered structures in the detection of retinal damage. Generalized estimating equations considering within-subject intereye relations were used to test for differences between the groups. A modified p value of <0.001 was considered statistically significant. Receiver operating characteristic (ROC) curves were constructed to describe the ability of fractal dimension to discriminate between the eyes of DM, MDR and healthy eyes. Significant decreases of fractal dimension were observed in all layers in the MDR eyes compared with controls except in the inner nuclear layer (INL). Significant decreases of fractal dimension were also observed in all layers in the MDR eyes compared with DM eyes. The highest area under receiver operating characteristic curve (AUROC) values estimated for fractal dimension were observed for the outer plexiform layer (OPL) and outer segment photoreceptors (OS) when comparing MDR eyes with controls. The highest AUROC value estimated for fractal dimension were also observed for the retinal nerve fiber layer (RNFL) and OS when comparing MDR eyes with DM eyes. Our results suggest that fractal dimension of the intraretinal layers may provide useful
Fractal dimension analysis of cerebellum in Chiari Malformation type I.
Akar, Engin; Kara, Sadık; Akdemir, Hidayet; Kırış, Adem
2015-09-01
Chiari Malformation type I (CM-I) is a serious neurological disorder that is characterized by hindbrain herniation. Our aim was to evaluate the usefulness of fractal analysis in CM-I patients. To examine the morphological complexity features of this disorder, fractal dimension (FD) of cerebellar regions were estimated from magnetic resonance images (MRI) of 17 patients with CM-I and 16 healthy control subjects in this study. The areas of white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF) were calculated and the corresponding FD values were computed using a 2D box-counting method in both groups. The results indicated that CM-I patients had significantly higher (p<0.05) FD values of GM, WM and CSF tissues compared to control group. According to the results of correlation analysis between FD values and the corresponding area values, FD and area values of GM tissues in the patients group were found to be correlated. The results of the present study suggest that FD values of cerebellar regions may be a discriminative feature and a useful marker for investigation of abnormalities in the cerebellum of CM-I patients. Further studies to explore the changes in cerebellar regions with the help of 3D FD analysis and volumetric calculations should be performed as a future work. PMID:26189156
Fractal Dimensions of In Vitro Tumor Cell Proliferation
Lambrou, George I.
2015-01-01
Biological systems are characterized by their potential for dynamic adaptation. One of the challenges for systems biology approaches is their contribution towards the understanding of the dynamics of a growing cell population. Conceptualizing these dynamics in tumor models could help us understand the steps leading to the initiation of the disease and its progression. In vitro models are useful in answering this question by providing information over the spatiotemporal nature of such dynamics. In the present work, we used physical quantities such as growth rate, velocity, and acceleration for the cellular proliferation and identified the fractal structures in tumor cell proliferation dynamics. We provide evidence that the rate of cellular proliferation is of nonlinear nature and exhibits oscillatory behavior. We also calculated the fractal dimensions of our cellular system. Our results show that the temporal transitions from one state to the other also follow nonlinear dynamics. Furthermore, we calculated self-similarity in cellular proliferation, providing the basis for further investigation in this topic. Such systems biology approaches are very useful in understanding the nature of cellular proliferation and growth. From a clinical point of view, our results may be applicable not only to primary tumors but also to tumor metastases. PMID:25883653
Smitha, K A; Gupta, A K; Jayasree, R S
2015-09-01
Glioma, the heterogeneous tumors originating from glial cells, generally exhibit varied grades and are difficult to differentiate using conventional MR imaging techniques. When this differentiation is crucial in the disease prognosis and treatment, even the advanced MR imaging techniques fail to provide a higher discriminative power for the differentiation of malignant tumor from benign ones. A powerful image processing technique applied to the imaging techniques is expected to provide a better differentiation. The present study focuses on the fractal analysis of fluid attenuation inversion recovery MR images, for the differentiation of glioma. For this, we have considered the most important parameters of fractal analysis, fractal dimension and lacunarity. While fractal analysis assesses the malignancy and complexity of a fractal object, lacunarity gives an indication on the empty space and the degree of inhomogeneity in the fractal objects. Box counting method with the preprocessing steps namely binarization, dilation and outlining was used to obtain the fractal dimension and lacunarity in glioma. Statistical analysis such as one-way analysis of variance and receiver operating characteristic (ROC) curve analysis helped to compare the mean and to find discriminative sensitivity of the results. It was found that the lacunarity of low and high grade gliomas vary significantly. ROC curve analysis between low and high grade glioma for fractal dimension and lacunarity yielded 70.3% sensitivity and 66.7% specificity and 70.3% sensitivity and 88.9% specificity, respectively. The study observes that fractal dimension and lacunarity increases with an increase in the grade of glioma and lacunarity is helpful in identifying most malignant grades. PMID:26305773
Sub-optimal MCV Cover Based Method for Measuring Fractal Dimension
Tolle, Charles Robert; McJunkin, Timothy R; Gorsich, D. I.
2003-01-01
A new method for calculating fractal dimension is developed in this paper. The method is based on the box dimension concept; however, it involves direct estimation of a suboptimal covering of the data set of interest. By finding a suboptimal cover, this method is better able to estimate the required number of covering elements for a given cover size than is the standard box counting algorithm. Moreover, any decrease in the error of the covering element count directly increases the accuracy of the fractal dimension estimation. In general, our method represents a mathematical dual to the standard box counting algorithm by not solving for the number of boxes used to cover a data set given the size of the box. Instead, the method chooses the number of covering elements and then proceeds to find the placement of smallest hyperellipsoids that fully covers the data set. This method involves a variant of the Fuzzy-C Means clustering algorithm, as well as the use of the Minimum Cluster Volume clustering algorithm. A variety of fractal dimension estimators using this suboptimal covering method are discussed. Finally, these methods are compared to the standard box counting algorithm and wavelet-decomposition methods for calculating fractal dimension by using one-dimensional cantor dust sets and a set of standard Brownian random fractal images.
Age-related reduction of chromatin fractal dimension in toluidine blue - stained hepatocytes.
Pantic, Igor; Petrovic, Danica; Paunovic, Jovana; Vucevic, Danijela; Radosavljevic, Tatjana; Pantic, Senka
2016-07-01
In this study, we proposed a hypothesis that chromatin of mouse hepatocytes exhibits age-related reduction of fractal dimension. This hypothesis was based on previously published works demonstrating that complexity of biological systems such as tissues, decreases during the process of physiological aging. Liver tissue was obtained from 24 male mice divided into 3 age groups: 10-days-old (young, juvenile), 210-days-old (adult) and 390-days-old. The tissue was stained using a modification of toluidine blue (nucleic acid - specific) staining method. A total of 480 chromatin structures (20 for each animal) were analyzed. For each structure, the values of fractal dimension, lacunarity, textural angular second moment and inverse difference moment were calculated using ImageJ software and its plugins. The results indicated the age-related reduction in fractal dimension and increase in lacunarity (p<0.01). Fractal dimension is a potentially good indicator of age associated changes in chromatin structure. To our knowledge, this is the first study to show that fractal complexity of hepatocyte chromatin decreases during the process of physiological aging. Fractal analysis as a method could be useful in detection of small age-related changes in chromatin distribution not otherwise visible with naked eye on conventional tissue micrographs. PMID:27412950
Nonlinear analysis of EEG in major depression with fractal dimensions.
Akar, Saime A; Kara, Sadik; Agambayev, Sumeyra; Bilgic, Vedat
2015-08-01
Major depressive disorder (MDD) is a psychiatric mood disorder characterized by cognitive and functional impairments in attention, concentration, learning and memory. In order to investigate and understand its underlying neural activities and pathophysiology, EEG methodologies can be used. In this study, we estimated the nonlinearity features of EEG in MDD patients to assess the dynamical properties underlying the frontal and parietal brain activity. EEG data were obtained from 16 patients and 15 matched healthy controls. A wavelet-chaos methodology was used for data analysis. First, EEGs of subjects were decomposed into 5 EEG sub-bands by discrete wavelet transform. Then, both the Katz's and Higuchi's fractal dimensions (KFD and HFD) were calculated as complexity measures for full-band and sub-bands EEGs. Last, two-way analyses of variances were used to test EEG complexity differences on each fractality measures. As a result, a significantly increased complexity was found in both parietal and frontal regions of MDD patients. This significantly increased complexity was observed not only in full-band activity but also in beta and gamma sub-bands of EEG. The findings of the present study indicate the possibility of using the wavelet-chaos methodology to discriminate the EEGs of MDD patients from healthy controls. PMID:26738004
Fractal dimensions of laser doppler flowmetry time series.
Carolan-Rees, G; Tweddel, A C; Naka, K K; Griffith, T M
2002-01-01
Laser Doppler flowmetry (LDF) provides a non-invasive method of assessing cutaneous perfusion. As the microvasculature under the probe is not defined the measured flux cannot be given absolute units, but the technique has nevertheless proved valuable for assessing relative changes in perfusion in response to physiological stress. LDF signals normally show pronounced temporal variability, both as a consequence of the pulsatile nature of blood flow and local changes in dynamic vasomotor activity. The aim of the present study was to investigate the use of methods of nonlinear analysis in characterizing temporal fluctuations in LDF signals. Data were collected under standardised conditions from the forearm of 16 normal subjects at rest, during exercise and on recovery. Surrogate data was then generated from the original time series by phase randomization. Dispersional analysis demonstrated that the LDF data was fractal with two distinct scaling regions, thus allowing the calculation of a fractal dimension which decreased significantly from 1.23 +/- 0.09 to 1.04 +/- 0.02 during exercise. By contrast, dispersional analysis of the surrogate data showed no scaling region. PMID:11891142
Relationship between Fractal Dimension and Agreeability of Facial Imagery
NASA Astrophysics Data System (ADS)
Oyama-Higa, Mayumi; Miao, Tiejun; Ito, Tasuo
2007-11-01
Why do people feel happy and good or equivalently empathize more, with smiling face imageries than with ones of expressionless face? To understand what the essential factors are underlying imageries in relating to the feelings, we conducted an experiment by 84 subjects asked to estimate the degree of agreeability about expressionless and smiling facial images taken from 23 young persons to whom the subjects were no any pre-acquired knowledge. Images were presented one at a time to each subject who was asked to rank agreeability on a scale from 1 to 10. Fractal dimensions of facial images were obtained in order to characterize the complexity of the imageries by using of two types of fractal analysis methods, i.e., planar and cubic analysis methods, respectively. The results show a significant difference in the fractal dimension values between expressionless faces and smiling ones. Furthermore, we found a well correlation between the degree of agreeability and fractal dimensions, implying that the fractal dimension optically obtained in relation to complexity in imagery information is useful to characterize the psychological processes of cognition and awareness.
EEG signal features extraction based on fractal dimension.
Finotello, Francesca; Scarpa, Fabio; Zanon, Mattia
2015-08-01
The spread of electroencephalography (EEG) in countless applications has fostered the development of new techniques for extracting synthetic and informative features from EEG signals. However, the definition of an effective feature set depends on the specific problem to be addressed and is currently an active field of research. In this work, we investigated the application of features based on fractal dimension to a problem of sleep identification from EEG data. We demonstrated that features based on fractal dimension, including two novel indices defined in this work, add valuable information to standard EEG features and significantly improve sleep identification performance. PMID:26737209
Effect of Na+ on surface fractal dimension of compacted bentonite
NASA Astrophysics Data System (ADS)
Xiang, G. S.; Xu, Y. F.; Jiang, H.
2015-05-01
Compacted Tsukinuno bentonite was immersed into NaCl solutions of different concentrations in oedometers, and the surface fractal dimension of bentonite-saline association was measured by nitrogen adsorption isotherms. The application of the Frenkel-Halsey-Hill equation and the Neimark thermodynamic method to nitrogen adsorption isotherms indicated that the surface roughness was greater for the bentonite-saline association. The surface fractal dimension of bentonite increased in the NaCl solution with low Na+ concentration, but decreased at high Na+ concentration. This process was accompanied by the same tendency in specific surface area and microporosity with the presence of Na+ coating in the clay particles.
Mukherjee, Anika; Chan, Adrian D C; Keating, Sarah; Redline, Raymond W; Fritsch, Michael K; Machin, Geoffrey A; Cornejo-Palma, Daniel; de Nanassy, Joseph; El-Demellawy, Dina; von Dadelszen, Peter; Benton, Samantha J; Grynspan, David
2016-01-01
The distal villous hypoplasia (DVH) pattern is a placental correlate of fetal growth restriction. Because the pattern seems to involve less complexity than do appropriately developed placental villi, we postulated that it may be associated with lower fractal dimension-a mathematical measure of complexity. Our study objectives were to evaluate interobserver agreement related to the DVH pattern among expert pathologists and to determine whether pathologist classification of DVH correlates with fractal dimension. A study set of 30 images of placental parenchyma at ×4 magnification was created by a single pathologist from a digital slide archive. The images were graded for the DVH pattern according to pre-specified definitions and included 10 images graded as "no DVH" (grade = 0), 10 with mild to moderate DVH (grade = 1), and 10 with severe DVH (grade = 2). The images were randomly sorted and shown to a panel of 4 international experts who similarly graded the images for DVH. Weighted kappas were calculated. For each image, fractal dimension was calculated by the Box Counting method. The correlation coefficient between (1) the averaged DVH scores obtained by the 5 pathologists and (2) fractal dimension was calculated. The mean weighted kappa score among the observers was 0.59 (range: 0.42-0.70). The correlation coefficient between fractal dimension and the averaged DVH score was -0.915 (P < 0.001). Expert pathologists achieve fair to substantial agreement in grading DVH, indicating consensus on the definition of DVH. Distal villous hypoplasia correlates extremely well with fractal dimension and represents an objective measure for DVH. PMID:26275121
Electroencephalographic Fractal Dimension in Healthy Ageing and Alzheimer's Disease.
Smits, Fenne Margreeth; Porcaro, Camillo; Cottone, Carlo; Cancelli, Andrea; Rossini, Paolo Maria; Tecchio, Franca
2016-01-01
Brain activity is complex; a reflection of its structural and functional organization. Among other measures of complexity, the fractal dimension is emerging as being sensitive to neuronal damage secondary to neurological and psychiatric diseases. Here, we calculated Higuchi's fractal dimension (HFD) in resting-state eyes-closed electroencephalography (EEG) recordings from 41 healthy controls (age: 20-89 years) and 67 Alzheimer's Disease (AD) patients (age: 50-88 years), to investigate whether HFD is sensitive to brain activity changes typical in healthy aging and in AD. Additionally, we considered whether AD-accelerating effects of the copper fraction not bound to ceruloplasmin (also called "free" copper) are reflected in HFD fluctuations. The HFD measure showed an inverted U-shaped relationship with age in healthy people (R2 = .575, p < .001). Onset of HFD decline appeared around the age of 60, and was most evident in central-parietal regions. In this region, HFD decreased with aging stronger in the right than in the left hemisphere (p = .006). AD patients demonstrated reduced HFD compared to age- and education-matched healthy controls, especially in temporal-occipital regions. This was associated with decreasing cognitive status as assessed by mini-mental state examination, and with higher levels of non-ceruloplasmin copper. Taken together, our findings show that resting-state EEG complexity increases from youth to maturity and declines in healthy, aging individuals. In AD, brain activity complexity is further reduced in correlation with cognitive impairment. In addition, elevated levels of non-ceruloplasmin copper appear to accelerate the reduction of neural activity complexity. Overall, HDF appears to be a proper indicator for monitoring EEG-derived brain activity complexity in healthy and pathological aging. PMID:26872349
Aggregate fractal dimensions and thermal conduction in nanofluids
NASA Astrophysics Data System (ADS)
Gharagozloo, Patricia E.; Goodson, Kenneth E.
2010-10-01
The mechanism producing enhanced thermal conductivities of nanofluids has been the subject of much debate. The formation of aggregates allowing for percolation paths within the fluid has shown the most promise. This work studies the aggregate formation of a nanofluid and compares the results to earlier thermal conductivity measurements and Monte Carlo simulation results. Static light scattering is employed to measure the fractal dimension of aggregates formed in the nanofluid over time at various temperatures and concentrations. As expected, aggregates form more quickly at higher concentrations and temperatures, which explains the increased enhancement with temperature reported by other research groups. The permanent aggregates in the nanofluid are found to have a fractal dimension of 2.4 and the aggregate formations that grow over time are found to have a fractal dimension of 1.8, which is consistent with diffusion limited aggregation. Predictions indicate that as aggregates grow the viscosity increases at a faster rate than thermal conductivity making the highly aggregated nanofluids unfavorable, especially at the low fractal dimension of 1.8.
NASA Astrophysics Data System (ADS)
Wei, Wei; Cai, Jianchao; Hu, Xiangyun; Fan, Ping; Han, Qi; Lu, Jinge; Cheng, Chu-Lin; Zhou, Feng
2015-03-01
The fractal dimension of random walker (FDRW) is an important parameter for description of electrical conductivity in porous media. However, it is somewhat empirical in nature to calculate FDRW. In this paper, a simple relation between FDRW and tortuosity fractal dimension (TFD) of current streamlines is derived, and a novel method of computing TFD for different generations of two-dimensional Sierpinski carpet and three-dimensional Sierpinski sponge models is presented through the finite element method, then the FDRW can be accordingly predicted; the proposed relation clearly shows that there exists a linear relation between pore fractal dimension (PFD) and TFD, which may have great potential in analysis of transport properties in fractal porous media.
Liver ultrasound image classification by using fractal dimension of edge
NASA Astrophysics Data System (ADS)
Moldovanu, Simona; Bibicu, Dorin; Moraru, Luminita
2012-08-01
Medical ultrasound image edge detection is an important component in increasing the number of application of segmentation, and hence it has been subject of many studies in the literature. In this study, we have classified the liver ultrasound images (US) combining Canny and Sobel edge detectors with fractal analysis in order to provide an indicator about of the US images roughness. We intend to provide a classification rule of the focal liver lesions as: cirrhotic liver, liver hemangioma and healthy liver. For edges detection the Canny and Sobel operators were used. Fractal analyses have been applied for texture analysis and classification of focal liver lesions according to fractal dimension (FD) determined by using the Box Counting method. To assess the performance and accuracy rate of the proposed method the contrast-to-noise (CNR) is analyzed.
Effect of 3D fractal dimension on contact area and asperity interactions in elastoplastic contact
NASA Astrophysics Data System (ADS)
Jourani, Abdeljalil
2016-05-01
Few models are devoted to investigate the effect of 3D fractal dimension Ds on contact area and asperity interactions. These models used statistical approaches or two-dimensional deterministic simulations without considering the asperity interactions and elastic-plastic transition regime. In this study, a complete 3D deterministic model is adopted to simulate the contact between fractal surfaces which are generated using a modified two-variable Weierstrass-Mandelbrot function. This model incorporates the asperity interactions and considers the different deformation modes of surface asperities which range from entirely elastic through elastic-plastic to entirely plastic contact. The simulations reveal that the elastoplastic model is more appropriate to calculate the contact area ratio and pressure field. It is also shown that the influence of the asperity interactions cannot be neglected, especially at lower fractal dimension Ds and higher load.
Texture descriptor combining fractal dimension and artificial crawlers
NASA Astrophysics Data System (ADS)
Gonçalves, Wesley Nunes; Machado, Bruno Brandoli; Bruno, Odemir Martinez
2014-02-01
Texture is an important visual attribute used to describe images. There are many methods available for texture analysis. However, they do not capture the detail richness of the image surface. In this paper, we propose a new method to describe textures using the artificial crawler model. This model assumes that agents can interact with the environment and each other. Since this swarm system alone does not achieve a good discrimination, we developed a new method to increase the discriminatory power of artificial crawlers, together with the fractal dimension theory. Here, we estimated the fractal dimension by the Bouligand-Minkowski method due to its precision in quantifying structural properties of images. We validate our method on two texture datasets and the experimental results reveal that our method leads to highly discriminative textural features. The results indicate that our method can be used in different texture applications.
Predicting beauty: fractal dimension and visual complexity in art.
Forsythe, A; Nadal, M; Sheehy, N; Cela-Conde, C J; Sawey, M
2011-02-01
Visual complexity has been known to be a significant predictor of preference for artistic works for some time. The first study reported here examines the extent to which perceived visual complexity in art can be successfully predicted using automated measures of complexity. Contrary to previous findings the most successful predictor of visual complexity was Gif compression. The second study examined the extent to which fractal dimension could account for judgments of perceived beauty. The fractal dimension measure accounts for more of the variance in judgments of perceived beauty in visual art than measures of visual complexity alone, particularly for abstract and natural images. Results also suggest that when colour is removed from an artistic image observers are unable to make meaningful judgments as to its beauty. PMID:21241285
Fractal dimensions of flocs between clay particles and HAB organisms
NASA Astrophysics Data System (ADS)
Wang, Hongliang; Yu, Zhiming; Cao, Xihua; Song, Xiuxian
2011-05-01
The impact of harmful algal blooms (HABs) on public health and related economics have been increasing in many coastal regions of the world. Sedimentation of algal cells through flocculation with clay particles is a promising strategy for controlling HABs. Previous studies found that removal efficiency (RE) was influenced by many factors, including clay type and concentration, algal growth stage, and physiological aspects of HAB cells. To estimate the effect of morphological characteristics of the aggregates on HAB cell removal, fractal dimensions were measured and the RE of three species of HAB organism, Heterosigma akashiwo, Alexandrium tamarense, and Skeletonema costatum, by original clay and modified clay, was determined. For all HAB species, the modified clay had a higher RE than original clay. For the original clay, the two-dimensional fractal dimension ( D 2) was 1.92 and three-dimensional fractal dimension ( D 3) 2.81, while for the modified clay, D 2 was 1.84 and D 3 was 2.50. The addition of polyaluminum chloride (PACl) lead to a decrease of the repulsive barrier between clay particles, and resulted in lower D 2 and D 3. Due to the decrease of D 3, and the increase of the effective sticking coefficient, the flocculation rate between modified clay particles and HAB organisms increased, and thus resulted in a high RE. The fractal dimensions of flocs differed in HAB species with different cell morphologies. For example, Alexandrium tamarense cells are ellipsoidal, and the D 3 and D 2 of flocs were the highest, while for Skeletonema costatum, which has filamentous cells, the D 3 and D 2 of flocs were the lowest.
Estimation of Fractal Dimension in Differential Diagnosis of Pigmented Skin Lesions
NASA Astrophysics Data System (ADS)
Aralica, Gorana; Milošević, Danko; Konjevoda, Paško; Seiwerth, Sven; Štambuk, Nikola
Medical differential diagnosis is a method of identifying the presence of a particular entity (disease) within a set of multiple possible alternatives. The significant problem in dermatology and pathology is the differential diagnosis of malignant melanoma and other pigmented skin lesions, especially of dysplastic nevi. Malignant melanoma is the most malignant skin neoplasma, with increasing incidence in various parts of the world. It is hoped that the methods of quantitative pathology, i.e. morphometry, can help objectification of the diagnostic process, since early discovery of melanoma results in 10-year survival rate of 90%. The aim of the study was to use fractal dimension calculated from the perimeter-area relation of the cell nuclei as a tool for the differential diagnosis of pigmented skin lesions. We analyzed hemalaun-eosin stained pathohistological slides of pigmented skin lesions: intradermal naevi (n = 45), dysplastic naevi (n = 47), and malignant melanoma (n = 50). It was found that fractal dimension of malignant melanoma cell nuclei differs significantly from the intradermal and dysplastic naevi (p ≤ 0. 001, Steel-Dwass Multiple Comparison Test). Additionaly, ROC analysis confirmed the value of fractal dimension based evaluation. It is suggested that the estimation of fractal dimension from the perimeter-area relation of the cell nuclei may be a potentially useful morphometric parameter in the medical differential diagnosis of pigmented skin lesions.
Mapping soil fractal dimension in agricultural fields with GPR
NASA Astrophysics Data System (ADS)
Oleschko, K.; Korvin, G.; Muñoz, A.; Velazquez, J.; Miranda, M. E.; Carreon, D.; Flores, L.; Martínez, M.; Velásquez-Valle, M.; Brambila, F.; Parrot, J.-F.; Ronquillo, G.
2008-09-01
We documented that the mapping of the fractal dimension of the backscattered Ground Penetrating Radar traces (Fractal Dimension Mapping, FDM) accomplished over heterogeneous agricultural fields gives statistically sound combined information about the spatial distribution of Andosol' dielectric permittivity, volumetric and gravimetric water content, bulk density, and mechanical resistance under seven different management systems. The roughness of the recorded traces was measured in terms of a single number H, the Hurst exponent, which integrates the competitive effects of volumetric water content, pore topology and mechanical resistance in space and time. We showed the suitability to combine the GPR traces fractal analysis with routine geostatistics (kriging) in order to map the spatial variation of soil properties by nondestructive techniques and to quantify precisely the differences under contrasting tillage systems. Three experimental plots with zero tillage and 33, 66 and 100% of crop residues imprinted the highest roughness to GPR wiggle traces (mean HR/S=0.15), significantly different to Andosol under conventional tillage (HR/S=0.47).
Surface evaluation by estimation of fractal dimension and statistical tools.
Hotar, Vlastimil; Salac, Petr
2014-01-01
Structured and complex data can be found in many applications in research and development, and also in industrial practice. We developed a methodology for describing the structured data complexity and applied it in development and industrial practice. The methodology uses fractal dimension together with statistical tools and with software modification is able to analyse data in a form of sequence (signals, surface roughness), 2D images, and dividing lines. The methodology had not been tested for a relatively large collection of data. For this reason, samples with structured surfaces produced with different technologies and properties were measured and evaluated with many types of parameters. The paper intends to analyse data measured by a surface roughness tester. The methodology shown compares standard and nonstandard parameters, searches the optimal parameters for a complete analysis, and specifies the sensitivity to directionality of samples for these types of surfaces. The text presents application of fractal geometry (fractal dimension) for complex surface analysis in combination with standard roughness parameters (statistical tool). PMID:25250380
Surface Evaluation by Estimation of Fractal Dimension and Statistical Tools
Salac, Petr
2014-01-01
Structured and complex data can be found in many applications in research and development, and also in industrial practice. We developed a methodology for describing the structured data complexity and applied it in development and industrial practice. The methodology uses fractal dimension together with statistical tools and with software modification is able to analyse data in a form of sequence (signals, surface roughness), 2D images, and dividing lines. The methodology had not been tested for a relatively large collection of data. For this reason, samples with structured surfaces produced with different technologies and properties were measured and evaluated with many types of parameters. The paper intends to analyse data measured by a surface roughness tester. The methodology shown compares standard and nonstandard parameters, searches the optimal parameters for a complete analysis, and specifies the sensitivity to directionality of samples for these types of surfaces. The text presents application of fractal geometry (fractal dimension) for complex surface analysis in combination with standard roughness parameters (statistical tool). PMID:25250380
Effect of mobile phone radiation on brain using EEG analysis by Higuichi's fractal dimension method
NASA Astrophysics Data System (ADS)
Smitha, C. K.; Narayanan, N. K.
2013-01-01
venient window on the mind, revealing synaptic action that is moderately to strongly co-relate with brain state. Fractal dimension, measure of signal complexity can be used to characterize the physiological conditions of the brain. As the EEG signal is non linear, non stationary and noisy, non linear methods will be suitable for the analysis. In this paper Higuichi's fractal method is applied to find the fractal dimension. EEGs of 5 volunteers were recorded at rest and on exposure to radiofrequency (RF) emissions from mobile phones having different SAR values. Mobiles were positioned near the ears and then near the cz position. Fractal dimensions for all conditions are calculated using Higuich's FD estimation algorithm. The result shows that there are some changes in the FD while using mobile phone. The change in FD of the signal varies from person to person. The changes in FD show the variations in EEG signal while using mobile phone, which demonstrate transformation in the activities of brain due to radiation.
Estimating the level of dynamical noise in time series by using fractal dimensions
NASA Astrophysics Data System (ADS)
Sase, Takumi; Ramírez, Jonatán Peña; Kitajo, Keiichi; Aihara, Kazuyuki; Hirata, Yoshito
2016-03-01
We present a method for estimating the dynamical noise level of a 'short' time series even if the dynamical system is unknown. The proposed method estimates the level of dynamical noise by calculating the fractal dimensions of the time series. Additionally, the method is applied to EEG data to demonstrate its possible effectiveness as an indicator of temporal changes in the level of dynamical noise.
NASA Astrophysics Data System (ADS)
Tijera, Manuel; Maqueda, Gregorio; Cano, José L.; López, Pilar; Yagüe, Carlos
2010-05-01
The wind velocity series of the atmospheric turbulent flow in the planetary boundary layer (PBL), in spite of being highly erratic, present a self-similarity structure (Frisch, 1995; Peitgen et., 2004; Falkovich et., 2006). So, the wind velocity can be seen as a fractal magnitude. We calculate the fractal dimension (Komolgorov capacity or box-counting dimension) of the wind perturbation series (u' = u- ) in the physical spaces (namely velocity-time). It has been studied the time evolution of the fractal dimension along different days and at three levels above the ground (5.8 m, 13.5 m, 32 m). The data analysed was recorded in the experimental campaign SABLES-98 (Cuxart et al., 2000) at the Research Centre for the Lower Atmosphere (CIBA) located in Valladolid (Spain). In this work the u, v and w components of wind velocity series have been measured by sonic anemometers (20 Hz sampling rate). The fractal dimension versus the integral length scales of the mean wind series have been studied, as well as the influence of different turbulent parameters. A method for estimating these integral scales is developed using the normalized autocorrelation function and a Gaussian fit. Finally, it will be analysed the variation of the fractal dimension versus stability parameters (as Richardson number) in order to explain some of the dominant features which are likely immersed in the fractal nature of these turbulent flows. References - Cuxart J, Yagüe C, Morales G, Terradellas E, Orbe J, Calvo J, Fernández A, Soler MR, Infante C, Buenestado P, Espinalt A, Joergensen HE, Rees JM, Vilá J, Redondo JM, Cantalapiedra IR and Conangla L (2000) Stable atmospheric boundary-layer experiment in Spain (SABLES98): a report. Boundary- Layer Meteorol 96:337-370 - Falkovich G and Kattepalli R. Sreenivasan (2006) Lessons from Hidrodynamic Turbulence. Physics Today 59: 43-49 - Frisch U (1995) Turbulence the legacy of A.N. Kolmogorov Cambridge University Press 269pp - Peitgen H, Jürgens H and
Fractal Dimensions for Radioisotope Pollution Patterns by Nuclear Power Plant Accidents
NASA Astrophysics Data System (ADS)
Saito, K.; Ogawa, S.
2015-04-01
The radioisotope pollution shows two types of patterns: dry and wet deposits for nuclear power plant accidents. Two surface pollution patterns were analysed by fractal. In Fukushima nuclear power plant accident, surface pollution by wet deposits was estimated to occur. However, actually it was no rain and white crystals were observed on the surface. Then, fractal analysis was carried out for the spatial distribution patterns of radio isotopes on the surface to judge the types of deposits. As a reference, Chernobyl nuclear power plant accident was checked for the spatial distribution patterns of radioisotopes on the surface. The objective patterns by fractal analysis were the surface pollution maps in Fukushima and Chernobyl, Abukuma river watershed map, and NOAA/AVHRR. The calculation of fractal dimensions was carried out with the box counting for binarized images. Fractal analysis results suggested the next conclusions. The radioisotope pollution in Fukushima might occur in both dry and wet deposits. The dry deposit might make the pollution pattern similar to the watershed, while the wet deposit might make the pollution pattern similar to cloud images. Moreover, most radioisotope contaminants might flow on the road in the forest valley and deposit on forest with and without rainfall in Fukushima.
Speech Emotion Recognition Based on Parametric Filter and Fractal Dimension
NASA Astrophysics Data System (ADS)
Mao, Xia; Chen, Lijiang
In this paper, we propose a new method that employs two novel features, correlation density (Cd) and fractal dimension (Fd), to recognize emotional states contained in speech. The former feature obtained by a list of parametric filters reflects the broad frequency components and the fine structure of lower frequency components, contributed by unvoiced phones and voiced phones, respectively; the latter feature indicates the non-linearity and self-similarity of a speech signal. Comparative experiments based on Hidden Markov Model and K Nearest Neighbor methods are carried out. The results show that Cd and Fd are much more closely related with emotional expression than the features commonly used.
Aggregation of liposomes in presence of La3+ : A study of the fractal dimension
NASA Astrophysics Data System (ADS)
Sabín, Juan; Prieto, Gerardo; Ruso, Juan M.; Messina, Paula; Sarmiento, Félix
2007-07-01
A study of the fractal dimension of the aggregation of three different types of large unilamellar vesicles, formed by egg yolk phosphatidylcholine (EYPC), dimyristoyl-phosphocholine (DMPC), and dipalmitoyl-phosphocholine (DPPC), in the presence of La3+ , is presented. Aggregate liposome fractal dimensions were calculated by two methods, aggregation kinetics, using the approaches diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA) and angle-scattering light dispersion. Electrophoretic measurements show a similar variation of the zeta potential ( ζ potential) for EYPC and DPPC, with a small increase of initial positive values. However, the ζ potential of DMPC changes from a initial negative value to near zero with increasing La3+ concentration. The evolution of the aggregate sizes was followed by light scattering. DPPC and DMPC show a RLCA regimen growth at low La3+ concentrations and a DLCA regimen at higher concentrations. In the case of EYPC, the final size of aggregation strongly depends on La3+ concentration. The calculated fractal dimension is in the range 1.8 to 2.1.
Hyper-Fractal Analysis: A visual tool for estimating the fractal dimension of 4D objects
NASA Astrophysics Data System (ADS)
Grossu, I. V.; Grossu, I.; Felea, D.; Besliu, C.; Jipa, Al.; Esanu, T.; Bordeianu, C. C.; Stan, E.
2013-04-01
This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images and 3D objects (Grossu et al. (2010) [1]). The program was extended for working with four-dimensional objects stored in comma separated values files. This might be of interest in biomedicine, for analyzing the evolution in time of three-dimensional images. New version program summaryProgram title: Hyper-Fractal Analysis (Fractal Analysis v03) Catalogue identifier: AEEG_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 745761 No. of bytes in distributed program, including test data, etc.: 12544491 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 100M Classification: 14 Catalogue identifier of previous version: AEEG_v2_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 831-832 Does the new version supersede the previous version? Yes Nature of problem: Estimating the fractal dimension of 4D images. Solution method: Optimized implementation of the 4D box-counting algorithm. Reasons for new version: Inspired by existing applications of 3D fractals in biomedicine [3], we extended the optimized version of the box-counting algorithm [1, 2] to the four-dimensional case. This might be of interest in analyzing the evolution in time of 3D images. The box-counting algorithm was extended in order to support 4D objects, stored in comma separated values files. A new form was added for generating 2D, 3D, and 4D test data. The application was tested on 4D objects with known dimension, e.g. the Sierpinski hypertetrahedron gasket, Df=ln(5)/ln(2) (Fig. 1). The algorithm could be extended, with minimum effort, to
Lu, Xiao-long; Zheng, Qin; Yin, Xian-zhen; Xiao, Guang-qing; Liao, Zu-hua; Yang, Ming; Zhang, Ji-wen
2015-06-01
The shape and structure of granules are controlled by the granulation process, which is one of the main factors to determine the nature of the solid dosage forms. In this article, three kinds of granules of a traditional Chinese medicine for improving appetite and promoting digestion, namely, Jianwei Granules, were prepared using granulation technologies as pendular granulation, high speed stirring granulation, and fluidized bed granulation and the powder properties of them were investigated. Meanwhile, synchrotron radiation X-ray computed micro tomography (SR-µCT) was applied to quantitatively determine the irregular internal structures of the granules. The three-dimensional (3D) structure models were obtained by 3D reconstruction, which were more accurately to characterize the three-dimensional structures of the particles through the quantitative data. The models were also used to quantitatively compare the structural differences of granules prepared by different granulation processes with the same formula, so as to characterize how the production process plays a role in the pharmaceutical behaviors of the granules. To focus on the irregularity of the particle structure, the box counting method was used to calculate the fractal dimensions of the granules. The results showed that the fractal dimension is more sensitive to reflect the minor differences in the structure features than the conventional parameters, and capable to specifically distinct granules in structure. It is proved that the fractal dimension could quantitatively characterize the structural information of irregular granules. It is the first time suggested by our research that the fractal dimension difference (Df,c) between two fractal dimension parameters, namely, the volume matrix fractal dimension and the surface matrix fractal dimension, is a new index to characterize granules with irregular structures and evaluate the effects of production processes on the structures of granules as a new
Application of fractal dimensions to study the structure of flocs formed in lime softening process.
Vahedi, Arman; Gorczyca, Beata
2011-01-01
The use of fractal dimensions to study the internal structure and settling of flocs formed in lime softening process was investigated. Fractal dimensions of flocs were measured directly on floc images and indirectly from their settling velocity. An optical microscope with a motorized stage was used to measure the fractal dimensions of lime softening flocs directly on their images in 2 and 3D space. The directly determined fractal dimensions of the lime softening flocs were 1.11-1.25 for floc boundary, 1.82-1.99 for cross-sectional area and 2.6-2.99 for floc volume. The fractal dimension determined indirectly from the flocs settling rates was 1.87 that was different from the 3D fractal dimension determined directly on floc images. This discrepancy is due to the following incorrect assumptions used for fractal dimensions determined from floc settling rates: linear relationship between square settling velocity and floc size (Stokes' Law), Euclidean relationship between floc size and volume, constant fractal dimensions and one primary particle size describing entire population of flocs. Floc settling model incorporating variable floc fractal dimensions as well as variable primary particle size was found to describe the settling velocity of large (>50 μm) lime softening flocs better than Stokes' Law. Settling velocities of smaller flocs (<50 μm) could still be quite well predicted by Stokes' Law. The variation of fractal dimensions with lime floc size in this study indicated that two mechanisms are involved in the formation of these flocs: cluster-cluster aggregation for small flocs (<50 μm) and diffusion-limited aggregation for large flocs (>50 μm). Therefore, the relationship between the floc fractal dimension and floc size appears to be determined by floc formation mechanisms. PMID:20937512
Laaksonen, Ari; Malila, Jussi; Nenes, Athanasios; Hung, Hui-Ming; Chen, Jen-Ping
2016-01-01
Surface porosity affects the ability of a substance to adsorb gases. The surface fractal dimension D is a measure that indicates the amount that a surface fills a space, and can thereby be used to characterize the surface porosity. Here we propose a new method for determining D, based on measuring both the water vapour adsorption isotherm of a given substance, and its ability to act as a cloud condensation nucleus when introduced to humidified air in aerosol form. We show that our method agrees well with previous methods based on measurement of nitrogen adsorption. Besides proving the usefulness of the new method for general surface characterization of materials, our results show that the surface fractal dimension is an important determinant in cloud drop formation on water insoluble particles. We suggest that a closure can be obtained between experimental critical supersaturation for cloud drop activation and that calculated based on water adsorption data, if the latter is corrected using the surface fractal dimension of the insoluble cloud nucleus. PMID:27138171
NASA Astrophysics Data System (ADS)
Laaksonen, Ari; Malila, Jussi; Nenes, Athanasios; Hung, Hui-Ming; Chen, Jen-Ping
2016-05-01
Surface porosity affects the ability of a substance to adsorb gases. The surface fractal dimension D is a measure that indicates the amount that a surface fills a space, and can thereby be used to characterize the surface porosity. Here we propose a new method for determining D, based on measuring both the water vapour adsorption isotherm of a given substance, and its ability to act as a cloud condensation nucleus when introduced to humidified air in aerosol form. We show that our method agrees well with previous methods based on measurement of nitrogen adsorption. Besides proving the usefulness of the new method for general surface characterization of materials, our results show that the surface fractal dimension is an important determinant in cloud drop formation on water insoluble particles. We suggest that a closure can be obtained between experimental critical supersaturation for cloud drop activation and that calculated based on water adsorption data, if the latter is corrected using the surface fractal dimension of the insoluble cloud nucleus.
Laaksonen, Ari; Malila, Jussi; Nenes, Athanasios; Hung, Hui-Ming; Chen, Jen-Ping
2016-01-01
Surface porosity affects the ability of a substance to adsorb gases. The surface fractal dimension D is a measure that indicates the amount that a surface fills a space, and can thereby be used to characterize the surface porosity. Here we propose a new method for determining D, based on measuring both the water vapour adsorption isotherm of a given substance, and its ability to act as a cloud condensation nucleus when introduced to humidified air in aerosol form. We show that our method agrees well with previous methods based on measurement of nitrogen adsorption. Besides proving the usefulness of the new method for general surface characterization of materials, our results show that the surface fractal dimension is an important determinant in cloud drop formation on water insoluble particles. We suggest that a closure can be obtained between experimental critical supersaturation for cloud drop activation and that calculated based on water adsorption data, if the latter is corrected using the surface fractal dimension of the insoluble cloud nucleus. PMID:27138171
Analysis of fractal dimensions of rat bones from film and digital images
NASA Technical Reports Server (NTRS)
Pornprasertsuk, S.; Ludlow, J. B.; Webber, R. L.; Tyndall, D. A.; Yamauchi, M.
2001-01-01
OBJECTIVES: (1) To compare the effect of two different intra-oral image receptors on estimates of fractal dimension; and (2) to determine the variations in fractal dimensions between the femur, tibia and humerus of the rat and between their proximal, middle and distal regions. METHODS: The left femur, tibia and humerus from 24 4-6-month-old Sprague-Dawley rats were radiographed using intra-oral film and a charge-coupled device (CCD). Films were digitized at a pixel density comparable to the CCD using a flat-bed scanner. Square regions of interest were selected from proximal, middle, and distal regions of each bone. Fractal dimensions were estimated from the slope of regression lines fitted to plots of log power against log spatial frequency. RESULTS: The fractal dimensions estimates from digitized films were significantly greater than those produced from the CCD (P=0.0008). Estimated fractal dimensions of three types of bone were not significantly different (P=0.0544); however, the three regions of bones were significantly different (P=0.0239). The fractal dimensions estimated from radiographs of the proximal and distal regions of the bones were lower than comparable estimates obtained from the middle region. CONCLUSIONS: Different types of image receptors significantly affect estimates of fractal dimension. There was no difference in the fractal dimensions of the different bones but the three regions differed significantly.
Wang Xujing; Becker, Frederick F.; Gascoyne, Peter R. C.
2010-12-15
The scale-invariant property of the cytoplasmic membrane of biological cells is examined by applying the Minkowski-Bouligand method to digitized scanning electron microscopy images of the cell surface. The membrane is found to exhibit fractal behavior, and the derived fractal dimension gives a good description of its morphological complexity. Furthermore, we found that this fractal dimension correlates well with the specific membrane dielectric capacitance derived from the electrorotation measurements. Based on these findings, we propose a new fractal single-shell model to describe the dielectrics of mammalian cells, and compare it with the conventional single-shell model (SSM). We found that while both models fit with experimental data well, the new model is able to eliminate the discrepancy between the measured dielectric property of cells and that predicted by the SSM.
Scaling exponents for a monkey on a tree: fractal dimensions of randomly branched polymers.
Janssen, Hans-Karl; Stenull, Olaf
2012-05-01
We study asymptotic properties of diffusion and other transport processes (including self-avoiding walks and electrical conduction) on large, randomly branched polymers using renormalized dynamical field theory. We focus on the swollen phase and the collapse transition, where loops in the polymers are irrelevant. Here the asymptotic statistics of the polymers is that of lattice trees, and diffusion on them is reminiscent of the climbing of a monkey on a tree. We calculate a set of universal scaling exponents including the diffusion exponent and the fractal dimension of the minimal path to two-loop order and, where available, compare them to numerical results. PMID:23004722
NASA Astrophysics Data System (ADS)
Zeng, Qiang; Luo, Mingyong; Pang, Xiaoyun; Li, Le; Li, Kefei
2013-10-01
This study investigates the surface fractal dimensions (SFDs) of pore structure of cement pastes and mortars with/without ground granulated blast-furnace slag (GGBS) incorporated into binder. The samples were subject to water curing and sealed curing. The fractal dimensions of samples are determined by Zhang’s model (Ind Eng Chem Res, 34 (1995):1383-1386) on the basis of mercury intrusion porosimetry (MIP) data. The results confirm the scale-dependent property of fractal dimension of pore structures and the micro-fractal, transition and macro-fractal regions are identified for all samples. The upper pore size range for micro-fractal regions is around 30 nm, the transition regions cover 0.5-2 magnitude orders of pore size and macro fractal regions cover 1.5-3 magnitude orders. Both curing conditions and GGBS in binder have impact on the fractal properties of pore structure, and samples incorporating GGBS have substantially larger values for micro-fractal regions.
A Fractal Dimension and Wavelet Transform Based Method for Protein Sequence Similarity Analysis.
Yang, Lina; Tang, Yuan Yan; Lu, Yang; Luo, Huiwu
2015-01-01
One of the key tasks related to proteins is the similarity comparison of protein sequences in the area of bioinformatics and molecular biology, which helps the prediction and classification of protein structure and function. It is a significant and open issue to find similar proteins from a large scale of protein database efficiently. This paper presents a new distance based protein similarity analysis using a new encoding method of protein sequence which is based on fractal dimension. The protein sequences are first represented into the 1-dimensional feature vectors by their biochemical quantities. A series of Hybrid method involving discrete Wavelet transform, Fractal dimension calculation (HWF) with sliding window are then applied to form the feature vector. At last, through the similarity calculation, we can obtain the distance matrix, by which, the phylogenic tree can be constructed. We apply this approach by analyzing the ND5 (NADH dehydrogenase subunit 5) protein cluster data set. The experimental results show that the proposed model is more accurate than the existing ones such as Su's model, Zhang's model, Yao's model and MEGA software, and it is consistent with some known biological facts. PMID:26357222
Fractal Dimension Analysis of Subcortical Gray Matter Structures in Schizophrenia.
Zhao, Guihu; Denisova, Kristina; Sehatpour, Pejman; Long, Jun; Gui, Weihua; Qiao, Jianping; Javitt, Daniel C; Wang, Zhishun
2016-01-01
A failure of adaptive inference-misinterpreting available sensory information for appropriate perception and action-is at the heart of clinical manifestations of schizophrenia, implicating key subcortical structures in the brain including the hippocampus. We used high-resolution, three-dimensional (3D) fractal geometry analysis to study subtle and potentially biologically relevant structural alterations (in the geometry of protrusions, gyri and indentations, sulci) in subcortical gray matter (GM) in patients with schizophrenia relative to healthy individuals. In particular, we focus on utilizing Fractal Dimension (FD), a compact shape descriptor that can be computed using inputs with irregular (i.e., not necessarily smooth) surfaces in order to quantify complexity (of geometrical properties and configurations of structures across spatial scales) of subcortical GM in this disorder. Probabilistic (entropy-based) information FD was computed based on the box-counting approach for each of the seven subcortical structures, bilaterally, as well as the brainstem from high-resolution magnetic resonance (MR) images in chronic patients with schizophrenia (n = 19) and age-matched healthy controls (n = 19) (age ranges: patients, 22.7-54.3 and healthy controls, 24.9-51.6 years old). We found a significant reduction of FD in the left hippocampus (median: 2.1460, range: 2.07-2.18 vs. median: 2.1730, range: 2.15-2.23, p<0.001; Cohen's effect size, U3 = 0.8158 (95% Confidence Intervals, CIs: 0.6316, 1.0)), the right hippocampus (median: 2.1430, range: 2.05-2.19 vs. median: 2.1760, range: 2.12-2.21, p = 0.004; U3 = 0.8421 (CIs: 0.5263, 1)), as well as left thalamus (median: 2.4230, range: 2.40-2.44, p = 0.005; U3 = 0.7895 (CIs: 0.5789, 0.9473)) in schizophrenia patients, relative to healthy individuals. Our findings provide in-vivo quantitative evidence for reduced surface complexity of hippocampus, with reduced FD indicating a less complex, less regular GM surface detected in
Fractal Dimension Analysis of Subcortical Gray Matter Structures in Schizophrenia
Sehatpour, Pejman; Long, Jun; Gui, Weihua; Qiao, Jianping; Javitt, Daniel C.; Wang, Zhishun
2016-01-01
A failure of adaptive inference—misinterpreting available sensory information for appropriate perception and action—is at the heart of clinical manifestations of schizophrenia, implicating key subcortical structures in the brain including the hippocampus. We used high-resolution, three-dimensional (3D) fractal geometry analysis to study subtle and potentially biologically relevant structural alterations (in the geometry of protrusions, gyri and indentations, sulci) in subcortical gray matter (GM) in patients with schizophrenia relative to healthy individuals. In particular, we focus on utilizing Fractal Dimension (FD), a compact shape descriptor that can be computed using inputs with irregular (i.e., not necessarily smooth) surfaces in order to quantify complexity (of geometrical properties and configurations of structures across spatial scales) of subcortical GM in this disorder. Probabilistic (entropy-based) information FD was computed based on the box-counting approach for each of the seven subcortical structures, bilaterally, as well as the brainstem from high-resolution magnetic resonance (MR) images in chronic patients with schizophrenia (n = 19) and age-matched healthy controls (n = 19) (age ranges: patients, 22.7–54.3 and healthy controls, 24.9–51.6 years old). We found a significant reduction of FD in the left hippocampus (median: 2.1460, range: 2.07–2.18 vs. median: 2.1730, range: 2.15–2.23, p<0.001; Cohen’s effect size, U3 = 0.8158 (95% Confidence Intervals, CIs: 0.6316, 1.0)), the right hippocampus (median: 2.1430, range: 2.05–2.19 vs. median: 2.1760, range: 2.12–2.21, p = 0.004; U3 = 0.8421 (CIs: 0.5263, 1)), as well as left thalamus (median: 2.4230, range: 2.40–2.44, p = 0.005; U3 = 0.7895 (CIs: 0.5789, 0.9473)) in schizophrenia patients, relative to healthy individuals. Our findings provide in-vivo quantitative evidence for reduced surface complexity of hippocampus, with reduced FD indicating a less complex, less regular GM
NASA Astrophysics Data System (ADS)
Arefiev, K.; Nesterenko, V.; Daneykina, N.
2016-06-01
The results of communication research between the wear resistance of the K applicability hard-alloy cutting tools and the fractal dimension of the wear surface, which is formed on a back side of the cutting edge when processing the materials showing high adhesive activity are presented in the paper. It has been established that the wear resistance of tested cutting tools samples increases according to a fractal dimension increase of their wear surface.
The fractal dimensions of the spatial distribution of young open clusters in the solar neighbourhood
NASA Astrophysics Data System (ADS)
de La Fuente Marcos, R.; de La Fuente Marcos, C.
2006-06-01
Context: .Fractals are geometric objects with dimensionalities that are not integers. They play a fundamental role in the dynamics of chaotic systems. Observation of fractal structure in both the gas and the star-forming sites in galaxies suggests that the spatial distribution of young open clusters should follow a fractal pattern, too. Aims: .Here we investigate the fractal pattern of the distribution of young open clusters in the Solar Neighbourhood using a volume-limited sample from WEBDA and a multifractal analysis. By counting the number of objects inside spheres of different radii centred on clusters, we study the homogeneity of the distribution. Methods: .The fractal dimension D of the spatial distribution of a volume-limited sample of young open clusters is determined by analysing different moments of the count-in-cells. The spectrum of the Minkowski-Bouligand dimension of the distribution is studied as a function of the parameter q. The sample is corrected for dynamical effects. Results: .The Minkowski-Bouligand dimension varies with q in the range 0.71-1.77, therefore the distribution of young open clusters is fractal. We estimate that the average value of the fractal dimension is < D> = 1.7± 0.2 for the distribution of young open clusters studied. Conclusions: .The spatial distribution of young open clusters in the Solar Neighbourhood exhibits multifractal structure. The fractal dimension is time-dependent, increasing over time. The values found are consistent with the fractal dimension of star-forming sites in other spiral galaxies.
SU-D-BRA-04: Fractal Dimension Analysis of Edge-Detected Rectal Cancer CTs for Outcome Prediction
Zhong, H; Wang, J; Hu, W; Shen, L; Wan, J; Zhou, Z; Zhang, Z
2015-06-15
Purpose: To extract the fractal dimension features from edge-detected rectal cancer CTs, and to examine the predictability of fractal dimensions to outcomes of primary rectal cancer patients. Methods: Ninety-seven rectal cancer patients treated with neo-adjuvant chemoradiation were enrolled in this study. CT images were obtained before chemoradiotherapy. The primary lesions of the rectal cancer were delineated by experienced radiation oncologists. These images were extracted and filtered by six different Laplacian of Gaussian (LoG) filters with different filter values (0.5–3.0: from fine to coarse) to achieve primary lesions in different anatomical scales. Edges of the original images were found at zero-crossings of the filtered images. Three different fractal dimensions (box-counting dimension, Minkowski dimension, mass dimension) were calculated upon the image slice with the largest cross-section of the primary lesion. The significance of these fractal dimensions in survival, recurrence and metastasis were examined by Student’s t-test. Results: For a follow-up time of two years, 18 of 97 patients had experienced recurrence, 24 had metastasis, and 18 were dead. Minkowski dimensions under large filter values (2.0, 2.5, 3.0) were significantly larger (p=0.014, 0.006, 0.015) in patients with recurrence than those without. For metastasis, only box-counting dimensions under a single filter value (2.5) showed differences (p=0.016) between patients with and without. For overall survival, box-counting dimensions (filter values = 0.5, 1.0, 1.5), Minkowski dimensions (filter values = 0.5, 1.5, 2.0, 2,5) and mass dimensions (filter values = 1.5, 2.0) were all significant (p<0.05). Conclusion: It is feasible to extract shape information by edge detection and fractal dimensions analysis in neo-adjuvant rectal cancer patients. This information can be used to prognosis prediction.
Fractal dimension-bound spatio-temporal analysis of digital mammograms
NASA Astrophysics Data System (ADS)
Shanmugavadivu, P.; Sivakumar, V.; Sudhir, Rashmi
2016-02-01
A new Fractal Dimension-based diagnosis technique for the change detection and time-series analysis of masses in the temporal digital mammogram is presented in this paper. As the digital mammograms are confirmed as a reliable source for the prognosis of breast cancer, the demand for the development of precise computer aided detection techniques is constantly on the increase. This formed the basis for the development of this method using Fractal geometry, which is an efficient mathematical approach that deals with self-similar and irregular geometric objects called fractals. This work comprises of the detection of spatial masses using Fractal Hurst bound enhancement and segmentation of those temporal masses using Fractal Thresholding. The consultant radiologist's assessment of mass lesions forms the baseline for comparison and validation of the detected masses. Further, this research work performs temporal analysis of mass lesions, detected from the mammograms of the current and the respective prior view using the principle of Fractal Dimension. The precision of Fractal-dimension based temporal texture analysis of malignant masses of digital mammograms subsequently attributes to their characterization.
NASA Astrophysics Data System (ADS)
Neves, L. A.; Oliveira, F. R.; Peres, F. A.; Moreira, R. D.; Moriel, A. R.; de Godoy, M. F.; Murta Junior, L. O.
2011-03-01
This paper presents a method for the quantification of cellular rejection in endomyocardial biopsies of patients submitted to heart transplant. The model is based on automatic multilevel thresholding, which employs histogram quantification techniques, histogram slope percentage analysis and the calculation of maximum entropy. The structures were quantified with the aid of the multi-scale fractal dimension and lacunarity for the identification of behavior patterns in myocardial cellular rejection in order to determine the most adequate treatment for each case.
LFN, QPO and fractal dimension of X-ray light curves from black hole binaries
NASA Astrophysics Data System (ADS)
Prosvetov, Art; Grebenev, Sergey
The origin of the low frequency noise (LFN) and quasi-periodic oscillations (QPO) observed in X-ray flux of Galactic black hole binaries is still not recognized in spite of multiple studies and attempts to model this phenomenon. There are known correlations between the QPO frequency, X-ray power density, X-ray flux and spectral state of the system, but there is no model that can do these dependences understandable. For the low frequency (~1 Hz) QPO we still have no even an idea capable to explain their production and don't know even what part of an accretion disc is responsible for them. Here we attempted to measure the fractal dimension of X-ray light curves of several black hole X-ray binaries and to study its correlation with the frequency of quasi periodic oscillations observed in their X-ray light-curves. The fractal dimension is a measure of the space-filling capacity of the light curves' profile. To measure the fractal dimension we used R/S method, which is fast enough and has good reputation in financial analytic and materials sciences. We found that if no QPO were observed in X-ray flux from the particular source, the fractal dimension is equal to the unique value which is independent on the source, its luminosity or its spectral state. On the other hand if QPO were detected in the flux, the fractal dimension deviated from its usual value. Also, we found a clear correlation between the QPO frequency and the fractal dimension of the emission. The relationship between these two parameters is solid but nonlinear. We believe that the analysis of X-ray light curves of black hole binaries using the fractal dimension has a good scientific potential and may provide an addition information on the geometry of accretion flow and fundamental physical parameters of the system.
Fractal dimension analysis of weight-bearing bones of rats during skeletal unloading
NASA Technical Reports Server (NTRS)
Pornprasertsuk, S.; Ludlow, J. B.; Webber, R. L.; Tyndall, D. A.; Sanhueza, A. I.; Yamauchi, M.
2001-01-01
Fractal analysis was used to quantify changes in trabecular bone induced through the use of a rat tail-suspension model to simulate microgravity-induced osteopenia. Fractal dimensions were estimated from digitized radiographs obtained from tail-suspended and ambulatory rats. Fifty 4-month-old male Sprague-Dawley rats were divided into groups of 24 ambulatory (control) and 26 suspended (test) animals. Rats of both groups were killed after periods of 1, 4, and 8 weeks. Femurs and tibiae were removed and radiographed with standard intraoral films and digitized using a flatbed scanner. Square regions of interest were cropped at proximal, middle, and distal areas of each bone. Fractal dimensions were estimated from slopes of regression lines fitted to circularly averaged plots of log power vs. log spatial frequency. The results showed that the computed fractal dimensions were significantly greater for images of trabecular bones from tail-suspended groups than for ambulatory groups (p < 0.01) at 1 week. Periods between 1 and 4 weeks likewise yielded significantly different estimates (p < 0.05), consistent with an increase in bone loss. In the tibiae, the proximal regions of the suspended group produced significantly greater fractal dimensions than other regions (p < 0.05), which suggests they were more susceptible to unloading. The data are consistent with other studies demonstrating osteopenia in microgravity environments and the regional response to skeletal unloading. Thus, fractal analysis could be a useful technique to evaluate the structural changes of bone.
Fractal dimension analysis for spike detection in low SNR extracellular signals
NASA Astrophysics Data System (ADS)
Salmasi, Mehrdad; Büttner, Ulrich; Glasauer, Stefan
2016-06-01
Objective. Many algorithms have been suggested for detection and sorting of spikes in extracellular recording. Nevertheless, it is still challenging to detect spikes in low signal-to-noise ratios (SNR). We propose a spike detection algorithm that is based on the fractal properties of extracellular signals and can detect spikes in low SNR regimes. Semi-intact spikes are low-amplitude spikes whose shapes are almost preserved. The detection of these spikes can significantly enhance the performance of multi-electrode recording systems. Approach. Semi-intact spikes are simulated by adding three noise components to a spike train: thermal noise, inter-spike noise, and spike-level noise. We show that simulated signals have fractal properties which make them proper candidates for fractal analysis. Then we use fractal dimension as the main core of our spike detection algorithm and call it fractal detector. The performance of the fractal detector is compared with three frequently used spike detectors. Main results. We demonstrate that in low SNR, the fractal detector has the best performance and results in the highest detection probability. It is shown that, in contrast to the other three detectors, the performance of the fractal detector is independent of inter-spike noise power and that variations in spike shape do not alter its performance. Finally, we use the fractal detector for spike detection in experimental data and similar to simulations, it is shown that the fractal detector has the best performance in low SNR regimes. Significance. The detection of low-amplitude spikes provides more information about the neural activity in the vicinity of the recording electrodes. Our results suggest using the fractal detector as a reliable and robust method for detecting semi-intact spikes in low SNR extracellular signals.
Measurement of time-dependent fractal dimension for time series of silicon content in pig iron
NASA Astrophysics Data System (ADS)
Zhou, Zhi-Min
2007-03-01
This work applies the rescaled range analysis and fractal dimension technique to analyze the time series on silicon content in pig iron for detecting the inherent mechanism that governs blast furnace iron making process. The results show that there is time-dependent fractal feature and deterministic mechanism in blast furnace (BF) ironmaking process, which is helpful to gain deeper understanding of BF ironmaking process and also provide a powerful tool to solve the prediction of the silicon content in pig iron.
Crack detection in beams in noisy conditions using scale fractal dimension analysis of mode shapes
NASA Astrophysics Data System (ADS)
Bai, R. B.; Ostachowicz, W.; Cao, M. S.; Su, Z.
2014-06-01
Fractal dimension analysis of mode shapes has been actively studied in the area of structural damage detection. The most prominent features of fractal dimension analysis are high sensitivity to damage and instant determination of damage location. However, an intrinsic deficiency is its susceptibility to measurement noise, likely obscuring the features of damage. To address this deficiency, this study develops a novel damage detection method, scale fractal dimension (SFD) analysis of mode shapes, based on combining the complementary merits of a stationary wavelet transform (SWT) and Katz’s fractal dimension in damage characterization. With this method, the SWT is used to decompose a mode shape into a set of scale mode shapes at scale levels, with damage information and noise separated into distinct scale mode shapes because of their dissimilar scale characteristics; the Katz’s fractal dimension individually runs on every scale mode shape in the noise-adaptive condition provided by the SWT to canvass damage. Proof of concept for the SFD analysis is performed on cracked beams simulated by the spectral finite element method; the reliability of the method is assessed using Monte Carlo simulation to mimic the operational variability in realistic damage diagnosis. The proposed method is further experimentally validated on a cracked aluminum beam with mode shapes acquired by a scanning laser vibrometer. The results show that the SFD analysis of mode shapes provides a new strategy for damage identification in noisy conditions.
A modified radius fractal dimension for capturing spatial complexity of a polycentric city
NASA Astrophysics Data System (ADS)
Lan, Tian; Zhang, Hong; Wu, Xun; Cao, Weiwei; He, Jing
2015-12-01
As one of the most important indexes for describing spatial complexity of urban road networks, radius fractal dimension has been proved to be useful in single-central cities. The method needs to choose a traffic hub as the center of measurement, but if the city has more than one traffic center, it will be difficult to choose a proper center and portray spatial complexity of the whole road network. The modified method proposed in this paper regards all the nodes of a network as centers of measurement and considers the whole effect of traffic centers in a polycentric city, so the modified radius fractal dimension describes the spatial complexity of a road network from an overall perspective and overcomes the problem that the traditional method relies on only one center. The experimental results show the modified radius fractal dimension is reliable, which can describe urban road networks in a new perspective.
NASA Technical Reports Server (NTRS)
Emerson, Charles W.; Sig-NganLam, Nina; Quattrochi, Dale A.
2004-01-01
The accuracy of traditional multispectral maximum-likelihood image classification is limited by the skewed statistical distributions of reflectances from the complex heterogenous mixture of land cover types in urban areas. This work examines the utility of local variance, fractal dimension and Moran's I index of spatial autocorrelation in segmenting multispectral satellite imagery. Tools available in the Image Characterization and Modeling System (ICAMS) were used to analyze Landsat 7 imagery of Atlanta, Georgia. Although segmentation of panchromatic images is possible using indicators of spatial complexity, different land covers often yield similar values of these indices. Better results are obtained when a surface of local fractal dimension or spatial autocorrelation is combined as an additional layer in a supervised maximum-likelihood multispectral classification. The addition of fractal dimension measures is particularly effective at resolving land cover classes within urbanized areas, as compared to per-pixel spectral classification techniques.
Ramakrishnan; Sadana
1998-12-15
The diffusion-limited binding kinetics of antigen (analyte) in solution to antibody (receptor) immobilized on a biosensor surface is analyzed within a fractal framework. Most of the data presented are adequately described by a single-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot ("Scientific Graphing Procedure, User's Manual," Jandel Scientific, San Rafael, CA, 1993). A couple of examples of a dual-fractal analysis are also presented. It is of interest to note that the binding rate coefficient and the fractal dimension both exhibit changes in the same direction for the analyte-receptor systems analyzed. Binding rate coefficient expressions as a function of the fractal dimension developed for the analyte-receptor binding systems indicate the high sensitivity of the binding rate coefficient on the fractal dimension when both a single- and a dual-fractal analysis are used. For example, for a single-fractal analysis and for the binding of cell surface proteins from Helicobacter pylori strain in solution to sialyl-(alpha-2,3)-lactose-conjugated (20 mol%) polyacrylamide immobilized on a resonant mirror biosensor (S. Hirmo et al., Anal. Biochem. 257, 63, 1998), the order of dependence of the binding rate coefficient, k, on the fractal dimension, Df, was 14.15. The fractional order of dependence of the binding rate coefficient(s) on the fractal dimension(s) further reinforces the fractal nature of the system. The binding rate coefficient(s) expressions developed as a function of the fractal dimension(s) are of particular value since they provide a means to better control biosensor performance by linking it to the heterogeneity on the surface and further emphasize in a quantitative sense the importance of the nature of the surface in biosensor performance. Copyright 1998 Academic Press. PMID:9845690
Fractal dimension in butterflies' wings: a novel approach to understanding wing patterns?
Castrejón-Pita, A A; Sarmiento-Galán, A; Castrejón-Pita, J R; Castrejón-García, R
2005-05-01
The geometrical complexity in the wings of several, taxonomically different butterflies, is analyzed in terms of their fractal dimension. Preliminary results provide some evidence on important questions about the (dis)similarity of the wing patterns in terms of their fractal dimension. The analysis is restricted to two groups which are widely used in the literature as typical examples of mimicry, and a small number of unrelated species, thus implying the consideration of only a fraction of the wing pattern diversity. The members of the first mimicry ring, composed by the species Danaus plexippus (better known as the monarch butterfly), and the two subspecies Basilarchia archippus obsoleta (or northern viceroy) and Basilarchia archippus hoffmanni (or tropical viceroy), are found to have a very similar value for the fractal dimension of their wing patterns, even though they do not look very similar at first sight. It is also found that the female of another species (Neophasia terlootii), which looks similar to the members of the previous group, does not share the same feature, while the Lycorea ilione albescens does share it. For the members of the second group of mimicry related butterflies, the Greta nero nero and the Hypoleria cassotis, it is shown that they also have very close values for the fractal dimension of their wing patterns. Finally, it is shown that other species, which apparently have very similar wing patterns, do not have the same fractal dimension. A possible, not completely tested hypothesis is then conjectured: the formation of groups by individuals whose wing patterns have an almost equal fractal dimension may be due to the fact that they do share the same developmental raw material, and that this common feature is posteriorly modified by natural selection, possibly through predation. PMID:15614549
Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation
NASA Astrophysics Data System (ADS)
Santos, Andrés; de Haro, Mariano López
2016-06-01
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension d (1 ≤d ≤3 ) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for a fractal dimension [M. Heinen et al., Phys. Rev. Lett. 115, 097801 (2015), 10.1103/PhysRevLett.115.097801], a good agreement being observed.
Diagnosis System Based on Wavelet Transform, Fractal Dimension and Neural Network
NASA Astrophysics Data System (ADS)
El-Ramsisi, Abdallah M.; Khalil, Hassan A.
In this study we introduce a diagnosis system based on wavelet and fractal dimension for diagnose the Heart Mitral Valve Diseases. This study deals with the feature extraction from the Doppler signal waveform at heart mitral valve using ultrasound. Wavelet packet transforms, Fourier transform and Fractal Dimension methods are used for feature extraction from the DHS signals. The back-propagation neural network is used to classify the extracted features. The system has been evaluated in 162 samples that contain 89 normal and 73 abnormal. The results showed that the classification was about 91% for normal and abnormal cases.
Smith, R.L. Mecholsky, J.J.
2011-05-15
Fractal analysis has been used as a method to study fracture surfaces of brittle materials. However, it has not been determined if the fractal characteristics of brittle materials is consistent throughout the fracture surface. Therefore, the fractal dimensional increment of the mirror, mist, and hackle regions of the fracture surface of silica glass was determined using atomic force microscopy. The fractal dimensional increment of the mirror region (0.17-0.26) was determined to be statistically greater than that for the mist (0.08-0.12) and hackle (0.08-0.13) regions. It is thought that the increase in the fractal dimensional increment is caused by a greater tortuosity in the mirror region due to, most likely, the slower crack velocity of the propagating crack in that region and that there is a point between the mirror and mist region at which the fractal dimension decreases and becomes constant. - Research Highlights: {yields} The fracture surface of silica glass does not have a constant fractal dimension. {yields} Mirror region has greater fractal dimension than mist or hackle region. {yields} Fractal dimension decreases between mirror and mist region. {yields} Greater fractal dimension could be due to slower crack velocity in mirror region.
Electroencephalographic Fractal Dimension in Healthy Ageing and Alzheimer’s Disease
Cottone, Carlo; Cancelli, Andrea; Rossini, Paolo Maria; Tecchio, Franca
2016-01-01
Brain activity is complex; a reflection of its structural and functional organization. Among other measures of complexity, the fractal dimension is emerging as being sensitive to neuronal damage secondary to neurological and psychiatric diseases. Here, we calculated Higuchi’s fractal dimension (HFD) in resting-state eyes-closed electroencephalography (EEG) recordings from 41 healthy controls (age: 20–89 years) and 67 Alzheimer’s Disease (AD) patients (age: 50–88 years), to investigate whether HFD is sensitive to brain activity changes typical in healthy aging and in AD. Additionally, we considered whether AD-accelerating effects of the copper fraction not bound to ceruloplasmin (also called “free” copper) are reflected in HFD fluctuations. The HFD measure showed an inverted U-shaped relationship with age in healthy people (R2 = .575, p < .001). Onset of HFD decline appeared around the age of 60, and was most evident in central-parietal regions. In this region, HFD decreased with aging stronger in the right than in the left hemisphere (p = .006). AD patients demonstrated reduced HFD compared to age- and education-matched healthy controls, especially in temporal-occipital regions. This was associated with decreasing cognitive status as assessed by mini-mental state examination, and with higher levels of non-ceruloplasmin copper. Taken together, our findings show that resting-state EEG complexity increases from youth to maturity and declines in healthy, aging individuals. In AD, brain activity complexity is further reduced in correlation with cognitive impairment. In addition, elevated levels of non-ceruloplasmin copper appear to accelerate the reduction of neural activity complexity. Overall, HDF appears to be a proper indicator for monitoring EEG-derived brain activity complexity in healthy and pathological aging. PMID:26872349
Roth, Eric J; Gilbert, Benjamin; Mays, David C
2015-10-20
Experiments reveal a wide discrepancy between the permeability of porous media containing colloid deposits and the available predictive equations. Evidence suggests that this discrepancy results, in part, from the predictive equations failing to account for colloid deposit morphology. This article reports a series of experiments using static light scattering (SLS) to characterize colloid deposit morphology within refractive index matched (RIM) porous media during flow through a column. Real time measurements of permeability, specific deposit, deposit fractal dimension, and deposit radius of gyration, at different vertical positions, were conducted with initially clean porous media at various ionic strengths and fluid velocities. Decreased permeability (i.e., increased clogging) corresponded with higher specific deposit, lower fractal dimension, and smaller radius of gyration. During deposition, fractal dimension, radius of gyration, and permeability decreased with increasing specific deposit. During flushing with colloid-free fluid, these trends reversed, with increased fractal dimension, radius of gyration, and permeability. These observations suggest a deposition scenario in which large and uniform aggregates become deposits, which reduce porosity, lead to higher fluid shear forces, which then decompose the deposits, filling the pore space with small and dendritic fragments of aggregate. PMID:26412205
Fractal dimensions of soy protein nanoparticle aggregates determined by dynamic mechanical method
Technology Transfer Automated Retrieval System (TEKTRAN)
The fractal dimension of the protein aggregates can be estimated by dynamic mechanical methods when the particle aggregates are imbedded in a polymer matrix. Nanocomposites were formed by mixing hydrolyzed soy protein isolate (HSPI) nanoparticle aggregates with styrene-butadiene (SB) latex, followe...
Structural and Fractal Dimensions are Reliable Determinants of Grain Yield in Soybean
Technology Transfer Automated Retrieval System (TEKTRAN)
Reliable models are needed to describe plants with complex geometric structures, quantify the impact of management strategies on the plant’s geometric distribution in space and time, and predict yield as a function of fractal dimension. We measured growth and development variables on single soybean ...
Di Ieva, Antonio; Grizzi, Fabio; Ceva-Grimaldi, Giorgia; Russo, Carlo; Gaetani, Paolo; Aimar, Enrico; Levi, Daniel; Pisano, Patrizia; Tancioni, Flavio; Nicola, Giancarlo; Tschabitscher, Manfred; Dioguardi, Nicola; Baena, Riccardo Rodriguez y
2007-01-01
It is well known that angiogenesis is a complex process that accompanies neoplastic growth, but pituitary tumours are less vascularized than normal pituitary glands. Several analytical methods aimed at quantifying the vascular system in two-dimensional histological sections have been proposed, with very discordant results. In this study we investigated the non-Euclidean geometrical complexity of the two-dimensional microvasculature of normal pituitary glands and pituitary adenomas by quantifying the surface fractal dimension that measures its space-filling property. We found a statistical significant difference between the mean vascular surface fractal dimension estimated in normal versus adenomatous tissues (P = 0.01), normal versus secreting adenomatous tissues (P = 0.0003), and normal versus non-secreting adenomatous tissues (P = 0.047), whereas the difference between the secreting and non-secreting adenomatous tissues was not statistically significant. This study provides the first demonstration that fractal dimension is an objective and valid quantitator of the two-dimensional geometrical complexity of the pituitary gland microvascular network in physiological and pathological states. Further studies are needed to compare the vascular surface fractal dimension estimates in different subtypes of pituitary tumours and correlate them with clinical parameters in order to evaluate whether the distribution pattern of vascular growth is related to a particular state of the pituitary gland. PMID:17784937
Size and Fractal Dimension of Colloid Deposits in Model Porous Media
NASA Astrophysics Data System (ADS)
Roth, E. J.; Mays, D. C.; Gilbert, B.
2014-12-01
Colloids exert significant influence on subsurface hydrology, geochemistry, and microbiology. In particular, colloid deposits reduce permeability, triggering a reduction or realignment of flow. Since many subsurface processes are transport-limited, this reduction or realignment of flow, in turn, influences numerous chemical and biological processes. This work explores a conceptual model linking permeability with colloid deposit morphology, where deposit morphology is quantified by two metrics of the colloid deposit: (1) characteristic size and (2) fractal dimension. These two metrics are measured using static light scattering (SLS) within refractive index matched (RIM) porous media, into which a suspension of 100 nm carboxylate-modified polystyrene microspheres are eluted at constant flow. Scattering data are fitted with a two-parameter model that includes deposit fractal dimension, and with a three-parameter model that also includes deposit size. For each set of scattering measurements, the appropriate model is selected using the Akaike information criterion, and model errors are estimated using the bootstrap with 100 replicates. Results indicate two key findings. First, fractal dimensions generally decrease with time as additional colloids are eluted into the column, indicating a transition from more uniform to more dendritic deposits. Second, permeability reduction is associated with colloid deposits having smaller fractal dimensions, that is, with more dendritic and space-filling deposits. Modeling efforts are currently underway to correlate permeability with the underlying hydrodynamic and geochemical variables that determine colloid deposit morphology.
NASA Astrophysics Data System (ADS)
Jo, Junghyo; Hörnblad, Andreas; Kilimnik, German; Hara, Manami; Ahlgren, Ulf; Periwal, Vipul
2013-06-01
The islets of Langerhans, responsible for controlling blood glucose levels, are dispersed within the pancreas. A universal power law governing the fractal spatial distribution of islets in two-dimensional pancreatic sections has been reported. However, the fractal geometry in the actual three-dimensional pancreas volume, and the developmental process that gives rise to such a self-similar structure, has not been investigated. Here, we examined the three-dimensional spatial distribution of islets in intact mouse pancreata using optical projection tomography and found a power law with a fractal dimension of 2.1. Furthermore, based on two-dimensional pancreatic sections of human autopsies, we found that the distribution of human islets also follows a universal power law with a fractal dimension of 1.5 in adult pancreata, which agrees with the value previously reported in smaller mammalian pancreas sections. Finally, we developed a self-avoiding growth model for the development of the islet distribution and found that the fractal nature of the spatial islet distribution may be associated with the self-avoidance in the branching process of vascularization in the pancreas.
Fractal spatial distribution of pancreatic islets in three dimensions: a self-avoiding growth model
Jo, Junghyo; Hörnblad, Andreas; Kilimnik, German; Hara, Manami; Ahlgren, Ulf; Periwal, Vipul
2013-01-01
The islets of Langerhans, responsible for controlling blood glucose levels, are dispersed within the pancreas. A universal power law governing the fractal spatial distribution of islets in two-dimensional pancreatic sections has been reported. However, the fractal geometry in the actual three-dimensional pancreas volume, and the developmental process that gives rise to such a self-similar structure, have not been investigated. Here, we examined the three-dimensional spatial distribution of islets in intact mouse pancreata using optical projection tomography and found a power law with a fractal dimension, 2.1. Furthermore, based on two-dimensional pancreatic sections of human autopsies, we found that the distribution of human islets also follows a universal power law with fractal dimension 1.5 in adult pancreata, which agrees with the value previously reported in smaller mammalian pancreas sections. Finally, we developed a self-avoiding growth model for the development of the islet distribution and found that the fractal nature of the spatial islet distribution may be associated with the self-avoidance in the branching process of vascularization in the pancreas. PMID:23629025
Pacagnelli, Francis Lopes; Sabela, Ana Karênina Dias de Almeida; Mariano, Thaoan Bruno; Ozaki, Guilherme Akio Tamura; Castoldi, Robson Chacon; do Carmo, Edna Maria; Carvalho, Robson Francisco; Tomasi, Loreta Casquel; Okoshi, Katashi; Vanderlei, Luiz Carlos Marques
2016-01-01
Background Right-sided heart failure has high morbidity and mortality, and may be caused by pulmonary arterial hypertension. Fractal dimension is a differentiated and innovative method used in histological evaluations that allows the characterization of irregular and complex structures and the quantification of structural tissue changes. Objective To assess the use of fractal dimension in cardiomyocytes of rats with monocrotaline-induced pulmonary arterial hypertension, in addition to providing histological and functional analysis. Methods Male Wistar rats were divided into 2 groups: control (C; n = 8) and monocrotaline-induced pulmonary arterial hypertension (M; n = 8). Five weeks after pulmonary arterial hypertension induction with monocrotaline, echocardiography was performed and the animals were euthanized. The heart was dissected, the ventricles weighed to assess anatomical parameters, and histological slides were prepared and stained with hematoxylin/eosin for fractal dimension analysis, performed using box-counting method. Data normality was tested (Shapiro-Wilk test), and the groups were compared with non-paired Student t test or Mann Whitney test (p < 0.05). Results Higher fractal dimension values were observed in group M as compared to group C (1.39 ± 0.05 vs. 1.37 ± 0.04; p < 0.05). Echocardiography showed lower pulmonary artery flow velocity, pulmonary acceleration time and ejection time values in group M, suggesting function worsening in those animals. Conclusion The changes observed confirm pulmonary-arterial-hypertension-induced cardiac dysfunction, and point to fractal dimension as an effective method to evaluate cardiac morphological changes induced by ventricular dysfunction. PMID:27223643
NASA Astrophysics Data System (ADS)
Cervantes, F.; Gonzalez, J.; Real, C.; Hoyos, L.
2012-12-01
ABSTRACT: Chaotic invariants like fractal dimensions are used to characterize non-linear time series. The fractal dimension is an important characteristic of fractals that contains information about their geometrical structure at multiple scales. In this work four fractal dimension estimation algorithms are applied to non-linear time series. The algorithms employed are the Higuchi's algorithm, the Petrosian's algorithm, the Katz's Algorithm and the Box counting method. The analyzed time series are associated with natural phenomena, the Dst a geomagnetic index which monitors the world wide magnetic storm; the Dst index is a global indicator of the state of the Earth's geomagnetic activity. The time series used in this work show a behavior self-similar, which depend on the time scale of measurements. It is also observed that fractal dimensions may not be constant over all time scales.
Are fractal dimensions of the spatial distribution of mineral deposits meaningful?
Raines, G.L.
2008-01-01
It has been proposed that the spatial distribution of mineral deposits is bifractal. An implication of this property is that the number of deposits in a permissive area is a function of the shape of the area. This is because the fractal density functions of deposits are dependent on the distance from known deposits. A long thin permissive area with most of the deposits in one end, such as the Alaskan porphyry permissive area, has a major portion of the area far from known deposits and consequently a low density of deposits associated with most of the permissive area. On the other hand, a more equi-dimensioned permissive area, such as the Arizona porphyry permissive area, has a more uniform density of deposits. Another implication of the fractal distribution is that the Poisson assumption typically used for estimating deposit numbers is invalid. Based on datasets of mineral deposits classified by type as inputs, the distributions of many different deposit types are found to have characteristically two fractal dimensions over separate non-overlapping spatial scales in the range of 5-1000 km. In particular, one typically observes a local dimension at spatial scales less than 30-60 km, and a regional dimension at larger spatial scales. The deposit type, geologic setting, and sample size influence the fractal dimensions. The consequence of the geologic setting can be diminished by using deposits classified by type. The crossover point between the two fractal domains is proportional to the median size of the deposit type. A plot of the crossover points for porphyry copper deposits from different geologic domains against median deposit sizes defines linear relationships and identifies regions that are significantly underexplored. Plots of the fractal dimension can also be used to define density functions from which the number of undiscovered deposits can be estimated. This density function is only dependent on the distribution of deposits and is independent of the
NASA Astrophysics Data System (ADS)
Avellar, J.; Duarte, L. G. S.; da Mota, L. A. C. P.; de Melo, N.; Skea, J. E. F.
2012-09-01
A set of Maple routines is presented, fully compatible with the new releases of Maple (14 and higher). The package deals with the numerical evolution of dynamical systems and provide flexible plotting of the results. The package also brings an initial conditions generator, a numerical solver manager, and a focusing set of routines that allow for better analysis of the graphical display of the results. The novelty that the package presents an optional C interface is maintained. This allows for fast numerical integration, even for the totally inexperienced Maple user, without any C expertise being required. Finally, the package provides the routines to calculate the fractal dimension of boundaries (via box counting). New version program summary Program Title: Ndynamics Catalogue identifier: %Leave blank, supplied by Elsevier. Licensing provisions: no. Programming language: Maple, C. Computer: Intel(R) Core(TM) i3 CPU M330 @ 2.13 GHz. Operating system: Windows 7. RAM: 3.0 GB Keywords: Dynamical systems, Box counting, Fractal dimension, Symbolic computation, Differential equations, Maple. Classification: 4.3. Catalogue identifier of previous version: ADKH_v1_0. Journal reference of previous version: Comput. Phys. Commun. 119 (1999) 256. Does the new version supersede the previous version?: Yes. Nature of problem Computation and plotting of numerical solutions of dynamical systems and the determination of the fractal dimension of the boundaries. Solution method The default method of integration is a fifth-order Runge-Kutta scheme, but any method of integration present on the Maple system is available via an argument when calling the routine. A box counting [1] method is used to calculate the fractal dimension [2] of the boundaries. Reasons for the new version The Ndynamics package met a demand of our research community for a flexible and friendly environment for analyzing dynamical systems. All the user has to do is create his/her own Maple session, with the system to
Landmine detection using IR image segmentation by means of fractal dimension analysis
NASA Astrophysics Data System (ADS)
Abbate, Horacio A.; Gambini, Juliana; Delrieux, Claudio; Castro, Eduardo H.
2009-05-01
This work is concerned with buried landmines detection by long wave infrared images obtained during the heating or cooling of the soil and a segmentation process of the images. The segmentation process is performed by means of a local fractal dimension analysis (LFD) as a feature descriptor. We use two different LFD estimators, box-counting dimension (BC), and differential box counting dimension (DBC). These features are computed in a per pixel basis, and the set of features is clusterized by means of the K-means method. This segmentation technique produces outstanding results, with low computational cost.
Zone specific fractal dimension of retinal images as predictor of stroke incidence.
Aliahmad, Behzad; Kumar, Dinesh Kant; Hao, Hao; Unnikrishnan, Premith; Che Azemin, Mohd Zulfaezal; Kawasaki, Ryo; Mitchell, Paul
2014-01-01
Fractal dimensions (FDs) are frequently used for summarizing the complexity of retinal vascular. However, previous techniques on this topic were not zone specific. A new methodology to measure FD of a specific zone in retinal images has been developed and tested as a marker for stroke prediction. Higuchi's fractal dimension was measured in circumferential direction (FDC) with respect to optic disk (OD), in three concentric regions between OD boundary and 1.5 OD diameter from its margin. The significance of its association with future episode of stroke event was tested using the Blue Mountain Eye Study (BMES) database and compared against spectrum fractal dimension (SFD) and box-counting (BC) dimension. Kruskal-Wallis analysis revealed FDC as a better predictor of stroke (H = 5.80, P = 0.016, α = 0.05) compared with SFD (H = 0.51, P = 0.475, α = 0.05) and BC (H = 0.41, P = 0.520, α = 0.05) with overall lower median value for the cases compared to the control group. This work has shown that there is a significant association between zone specific FDC of eye fundus images with future episode of stroke while this difference is not significant when other FD methods are employed. PMID:25485298
Zone Specific Fractal Dimension of Retinal Images as Predictor of Stroke Incidence
Kumar, Dinesh Kant; Hao, Hao; Unnikrishnan, Premith; Kawasaki, Ryo; Mitchell, Paul
2014-01-01
Fractal dimensions (FDs) are frequently used for summarizing the complexity of retinal vascular. However, previous techniques on this topic were not zone specific. A new methodology to measure FD of a specific zone in retinal images has been developed and tested as a marker for stroke prediction. Higuchi's fractal dimension was measured in circumferential direction (FDC) with respect to optic disk (OD), in three concentric regions between OD boundary and 1.5 OD diameter from its margin. The significance of its association with future episode of stroke event was tested using the Blue Mountain Eye Study (BMES) database and compared against spectrum fractal dimension (SFD) and box-counting (BC) dimension. Kruskal-Wallis analysis revealed FDC as a better predictor of stroke (H = 5.80, P = 0.016, α = 0.05) compared with SFD (H = 0.51, P = 0.475, α = 0.05) and BC (H = 0.41, P = 0.520, α = 0.05) with overall lower median value for the cases compared to the control group. This work has shown that there is a significant association between zone specific FDC of eye fundus images with future episode of stroke while this difference is not significant when other FD methods are employed. PMID:25485298
Nuclear fractal dimension as a prognostic factor in oral squamous cell carcinoma.
Goutzanis, L; Papadogeorgakis, N; Pavlopoulos, P M; Katti, K; Petsinis, V; Plochoras, I; Pantelidaki, C; Kavantzas, N; Patsouris, E; Alexandridis, C
2008-04-01
Strong theoretical reasons exist for using fractal geometry in measurements of natural objects, including most objects studied in pathology. Indeed, fractal dimension provides a more precise and theoretically more appropriate approximation of their structure properties and especially their shape complexity. The aim of our study was to evaluate the nuclear fractal dimension (FD) in tissue specimens from patients with oral cavity carcinomas in order to assess its potential value as prognostic factor. Relationships between FD and other factors including clinicopathologic characteristics were also investigated. Histological sections from 48 oral squamous cell carcinomas as well as from 17 non-malignant mucosa specimens were stained with Hematoxylin-Eosin for pathological examination and with Feulgen for nuclear complexity evaluation. The sections were evaluated by image analysis using fractal analysis software to quantify nuclear FD by the box-counting method. Carcinomas presented higher mean values of FD compared to normal mucosa. Well differentiated neoplasms had lower FD values than poorly differentiated ones. FD was significantly correlated with the nuclear size. Patients with FD lower than the median value of the sample had statistically significant higher survival rates. Within the sample of patients studied, FD was proved to be an independent prognostic factor of survival in oral cancer patients. In addition this study provides evidence that there are several statistically significant correlations between FD and other morphometric characteristics or clinicopathologic factors in oral squamous cell carcinomas. PMID:17692559
Fractal Dimension and Vessel Complexity in Patients with Cerebral Arteriovenous Malformations
Reishofer, Gernot; Koschutnig, Karl; Enzinger, Christian; Ebner, Franz; Ahammer, Helmut
2012-01-01
The fractal dimension (FD) can be used as a measure for morphological complexity in biological systems. The aim of this study was to test the usefulness of this quantitative parameter in the context of cerebral vascular complexity. Fractal analysis was applied on ten patients with cerebral arteriovenous malformations (AVM) and ten healthy controls. Maximum intensity projections from Time-of-Flight MRI scans were analyzed using different measurements of FD, the Box-counting dimension, the Minkowski dimension and generalized dimensions evaluated by means of multifractal analysis. The physiological significance of this parameter was investigated by comparing values of FD first, with the maximum slope of contrast media transit obtained from dynamic contrast-enhanced MRI data and second, with the nidus size obtained from X-ray angiography data. We found that for all methods, the Box-counting dimension, the Minkowski dimension and the generalized dimensions FD was significantly higher in the hemisphere with AVM compared to the hemisphere without AVM indicating that FD is a sensitive parameter to capture vascular complexity. Furthermore we found a high correlation between FD and the maximum slope of contrast media transit and between FD and the size of the central nidus pointing out the physiological relevance of FD. The proposed method may therefore serve as an additional objective parameter, which can be assessed automatically and might assist in the complex workup of AVMs. PMID:22815946
Fractal dimension of cohesive sediment flocs at steady state under seven shear flow conditions
Zhu, Zhongfan; Yu, Jingshan; Wang, Hongrui; Dou, Jie; Wang, Cheng
2015-08-12
The morphological properties of kaolin flocs were investigated in a Couette-flow experiment at the steady state under seven shear flow conditions (shear rates of 5.36, 9.17, 14, 24, 31, 41 and 53 s^{-1}). These properties include a one-dimensional (1-D) fractal dimension (D_{1}), a two-dimensional (2-D) fractal dimension (D_{2}), a perimeter-based fractal dimension (D_{pf}) and an aspect ratio (AR). They were calculated based on the projected area (A), equivalent size, perimeter (P) and length (L) of the major axis of the floc determined through sample observation and an image analysis system. The parameter D_{2}, which characterizes the relationship between the projected area and the length of the major axis using a power function, A ∝ L^{D2}, increased from 1.73 ± 0.03, 1.72 ± 0.03, and 1.75 ± 0.04 in the low shear rate group (G = 5.36, 9.17, and 14 s^{-1}) to 1.92 ± 0.03, 1.82 ± 0.02, 1.85 ± 0.02, and 1.81 ± 0.02 in the high shear rate group (24, 31, 41 and 53 s^{-1}), respectively. The parameter D_{1} characterizes the relationship between the perimeter and length of the major axis by the function P ∝ L^{D1} and decreased from 1.52 ± 0.02, 1.48 ± 0.02, 1.55 ± 0.02, and 1.63 ± 0.02 in the low shear group (5.36, 9.17, 14 and 24 s^{-1}) to 1.45 ± 0.02, 1.39 ± 0.02, and 1.39 ± 0.02 in the high shear group (31, 41 and 53 s^{-1}), respectively. The results indicate that with increasing shear rates, the flocs become less elongated and that their boundary lines become tighter and more regular, caused by more breakages and possible restructurings of the flocs. The parameter D_{pf}, which is related to the perimeter and the projected area through the function , decreased as the shear rate increased almost linearly. The parameter AR, which is the ratio of the length of the major axis and equivalent diameter, decreased from 1.56, 1
Fractal dimension of cohesive sediment flocs at steady state under seven shear flow conditions
Zhu, Zhongfan; Yu, Jingshan; Wang, Hongrui; Dou, Jie; Wang, Cheng
2015-08-12
The morphological properties of kaolin flocs were investigated in a Couette-flow experiment at the steady state under seven shear flow conditions (shear rates of 5.36, 9.17, 14, 24, 31, 41 and 53 s-1). These properties include a one-dimensional (1-D) fractal dimension (D1), a two-dimensional (2-D) fractal dimension (D2), a perimeter-based fractal dimension (Dpf) and an aspect ratio (AR). They were calculated based on the projected area (A), equivalent size, perimeter (P) and length (L) of the major axis of the floc determined through sample observation and an image analysis system. The parameter D2, which characterizes the relationship between the projectedmore » area and the length of the major axis using a power function, A ∝ LD2, increased from 1.73 ± 0.03, 1.72 ± 0.03, and 1.75 ± 0.04 in the low shear rate group (G = 5.36, 9.17, and 14 s-1) to 1.92 ± 0.03, 1.82 ± 0.02, 1.85 ± 0.02, and 1.81 ± 0.02 in the high shear rate group (24, 31, 41 and 53 s-1), respectively. The parameter D1 characterizes the relationship between the perimeter and length of the major axis by the function P ∝ LD1 and decreased from 1.52 ± 0.02, 1.48 ± 0.02, 1.55 ± 0.02, and 1.63 ± 0.02 in the low shear group (5.36, 9.17, 14 and 24 s-1) to 1.45 ± 0.02, 1.39 ± 0.02, and 1.39 ± 0.02 in the high shear group (31, 41 and 53 s-1), respectively. The results indicate that with increasing shear rates, the flocs become less elongated and that their boundary lines become tighter and more regular, caused by more breakages and possible restructurings of the flocs. The parameter Dpf, which is related to the perimeter and the projected area through the function , decreased as the shear rate increased almost linearly. The parameter AR, which is the ratio of the length of the major axis and equivalent diameter, decreased from 1.56, 1.59, 1.53 and 1.51 in the low shear rate group to 1.43, 1.47 and 1.48 in the high shear rate group. These changes in Dpf and AR show that the flocs become
Schneider, Gerald Johannes; Vollnhals, V; Brandt, K; Roth, S V; Göritz, D
2010-09-01
The morphology of the precipitated silica VN3 filled in styrene butadiene rubber was studied as a function of the volume fraction Φ by means of small-angle X-ray scattering experiments. The wide q-range of 0.008 nm(-1)fractal dimension does not depend on Φ, and by that means experimentally proving that there is not necessarily a correlation between the mass fractal dimension and the cluster size. PMID:20831333
Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation.
Santos, Andrés; de Haro, Mariano López
2016-06-01
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension d (1≤d≤3) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for a fractal dimension [M. Heinen et al., Phys. Rev. Lett. 115, 097801 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.097801], a good agreement being observed. PMID:27415227
Reljin, Natasa; Reyes, Bersain A.; Chon, Ki H.
2015-01-01
In this paper, we propose the use of blanket fractal dimension (BFD) to estimate the tidal volume from smartphone-acquired tracheal sounds. We collected tracheal sounds with a Samsung Galaxy S4 smartphone, from five (N = 5) healthy volunteers. Each volunteer performed the experiment six times; first to obtain linear and exponential fitting models, and then to fit new data onto the existing models. Thus, the total number of recordings was 30. The estimated volumes were compared to the true values, obtained with a Respitrace system, which was considered as a reference. Since Shannon entropy (SE) is frequently used as a feature in tracheal sound analyses, we estimated the tidal volume from the same sounds by using SE as well. The evaluation of the performed estimation, using BFD and SE methods, was quantified by the normalized root-mean-squared error (NRMSE). The results show that the BFD outperformed the SE (at least twice smaller NRMSE was obtained). The smallest NRMSE error of 15.877% ± 9.246% (mean ± standard deviation) was obtained with the BFD and exponential model. In addition, it was shown that the fitting curves calculated during the first day of experiments could be successfully used for at least the five following days. PMID:25923929
Reljin, Natasa; Reyes, Bersain A; Chon, Ki H
2015-01-01
In this paper, we propose the use of blanket fractal dimension (BFD) to estimate the tidal volume from smartphone-acquired tracheal sounds. We collected tracheal sounds with a Samsung Galaxy S4 smartphone, from five (N = 5) healthy volunteers. Each volunteer performed the experiment six times; first to obtain linear and exponential fitting models, and then to fit new data onto the existing models. Thus, the total number of recordings was 30. The estimated volumes were compared to the true values, obtained with a Respitrace system, which was considered as a reference. Since Shannon entropy (SE) is frequently used as a feature in tracheal sound analyses, we estimated the tidal volume from the same sounds by using SE as well. The evaluation of the performed estimation, using BFD and SE methods, was quantified by the normalized root-mean-squared error (NRMSE). The results show that the BFD outperformed the SE (at least twice smaller NRMSE was obtained). The smallest NRMSE error of 15.877% ± 9.246% (mean ± standard deviation) was obtained with the BFD and exponential model. In addition, it was shown that the fitting curves calculated during the first day of experiments could be successfully used for at least the five following days. PMID:25923929
Earthquake frequency-magnitude distribution and fractal dimension in mainland Southeast Asia
NASA Astrophysics Data System (ADS)
Pailoplee, Santi; Choowong, Montri
2014-12-01
The 2004 Sumatra and 2011 Tohoku earthquakes highlighted the need for a more accurate understanding of earthquake characteristics in both regions. In this study, both the a and b values of the frequency-magnitude distribution (FMD) and the fractal dimension ( D C ) were investigated simultaneously from 13 seismic source zones recognized in mainland Southeast Asia (MLSEA). By using the completeness earthquake dataset, the calculated values of b and D C were found to imply variations in seismotectonic stress. The relationships of D C -b and D C -( a/ b) were investigated to categorize the level of earthquake hazards of individual seismic source zones, where the calibration curves illustrate a negative correlation between the D C and b values ( D c = 2.80 - 1.22 b) and a positive correlation between the D C and a/ b ratios ( D c = 0.27( a/ b) - 0.01) with similar regression coefficients ( R 2 = 0.65 to 0.68) for both regressions. According to the obtained relationships, the Hsenwi-Nanting and Red River fault zones revealed low-stress accumulations. Conversely, the Sumatra-Andaman interplate and intraslab, the Andaman Basin, and the Sumatra fault zone were defined as high-tectonic stress regions that may pose risks of generating large earthquakes in the future.
A new way of describing meiosis that uses fractal dimension to predict metaphase I
2005-01-01
Meiosis, the reductive nuclear division, is a continuum, but for purposes of communication, is described in stages. In sexually-reproducing organisms, including the dwarf mistletoe Arceuthobium americanum, prophase I of meiosis is prolonged (8 months for female A. americanum). Conversely, metaphase I, where chromosome pairs line up along a dividing cell's "equator", is relatively brief, difficult to predict, but critical regarding the random distribution of the paternal and maternal chromosomes in sexual organisms. However, descriptions of meiosis as either a continuum or stages are limited to qualitative observations. A quantification of meiosis can provide mathematical descriptors and allow for the prediction of when chromosomes reach the equator; this will not only be useful to researchers of cell division, but also to those requiring a large sample of metaphase I materials. Here, the probability-density function was used to calculate the fractal dimension of A. americanum nuclei undergoing early meiosis, and it predicted the onset of metaphase I by 2 days. PMID:16094465
NASA Astrophysics Data System (ADS)
Kovalnogov, Vladislav N.; Fedorov, Ruslan V.; Generalov, Dmitry A.; Khakhalev, Yury A.; Zolotov, Aleksandr N.
2016-06-01
The results of numerical and experimental studies of the structure and the frictional resistance of the turbulent flow with the effects obtained by using a modified model of the mixing Prandtl with the fractal dimension of pressure fluctuations. A construction of a cooled turbine blade was designed based on the results. The construction comprises a combined cooling and cylindrical cavity on the blade surface and the inner surface of the cooling channels.
Pereda, E; Gamundi, A; Rial, R; González, J
1998-07-01
The question of whether the finite values of the correlation dimension (D2), used as an index of EEG complexity are due to its chaotic nature or they reflect its behaviour as linearly-correlated noise, remains open. This report aims at clarifying this by measuring D2 and analysing the non-linear nature of EEG through the method of surrogate data as well as by calculating the fractal exponent (beta) via coarse graining spectral analysis (CGSA) in nine adult subjects during waking and sleep states. The results show that even if it is possible to get an estimation of D2 in all states, non-linear structure appears to be present only during slow wave sleep (SWS). EEG exhibits random fractal structure with 1/f(-beta) spectrum (1 < beta < 3) and a negative linear correlation between D2 and beta in all states except during SWS. In consequence, in those states, finite D2 values could be attributed to the fractal nature of EEG and not to the presence of low-dimensional chaos, and therefore, it the use of beta would be more appropriate to describe the complexity of EEG, due to its lower computational cost. PMID:9697926
NASA Astrophysics Data System (ADS)
Ohsasa, K.; Natsume, Y.; Sekiya, T.; Hatayama, T.
2015-06-01
The dendrite morphology of unidirectionally solidified Al-Si alloys was evaluated by measuring the fractal dimension and dimensionless perimeter of dendrites. In an unidirectional solidification experiment, columnar crystals grew from a bottom chill and columnar to equiaxed transition (CET) occurred at the upper part of an ingot. Then, equiaxed crystals were formed at the top of the ingot. Different dendrite morphology was observed in longitudinal, transverse and oblique sections, however, the fractal dimension or dimensionless perimiter of the dendrites in the sections with same local solidification time showed same values, and continuously decreased with increase in the local solidification time through columnar, CET and equiaxed regions. It can be considered that the fractal dimension and dimensionless perimiter of dendrites are controlled by local solidification time and irrespective of dendrite morphology. This result demonstrated the potential of the fractal dimension and dimensionless perimiter as a parameter for estimating local solidification time of an ingot in which the measurement of SDAS is difficult.
Pancheliuga, V A; Pancheliuga, M S
2013-01-01
In the present work a methodological background for the histogram method of time series analysis is developed. Connection between shapes of smoothed histograms constructed on the basis of short segments of time series of fluctuations and the fractal dimension of the segments is studied. It is shown that the fractal dimension possesses all main properties of the histogram method. Based on it a further development of fractal dimension determination algorithm is proposed. This algorithm allows more precision determination of the fractal dimension by using the "all possible combination" method. The application of the method to noise-like time series analysis leads to results, which could be obtained earlier only by means of the histogram method based on human expert comparisons of histograms shapes. PMID:23755565
Fractal dimension and surface topography on the diamond deposition of seeded WC-Co substrates
NASA Astrophysics Data System (ADS)
Chou, C.-C.; Lin, H.-H.
2010-04-01
Diamond thin films were deposited on WC-Co substrates by hot filament chemical vapor deposition to improve the tribological performance. The influence of the substrate surface topography was found to play an important role during the nucleation stage and the later growth rate as well. In this study, we systematically investigated the relation between substrate surface irregularity, which was evaluated by fractal dimension as well as statistical roughness parameters and the quality of the later deposited diamond film. Preseeding processes, in diamond acetone suspensions with two particle diameters, by supersonic vibrator were also implemented to investigate the effect of particular size on diamond nucleation. The original surfaces were measured with a stylus profiler and contact-mode atomic force microscopy. The diamond deposited substrates were examined by scanning electron microscopy, x-ray diffractometry, Raman spectroscopy, and Rockwell-C indentation to study substrate topography, crystalline structure of the coating, the composition of diamond films, and adhesion between deposited layers and substrates, respectively. The synergetic influence of the substrate's fractal dimension and the particular size of pre-seeding diamond suspension were studied and addressed. The deposited film of a WC-Co substrate with higher surface fractal dimension (>2.50), preseeded by fine diamond suspension (4-12 nm particle size) in advance, has a high diamond-rich composition and adhesion strength.
Gheonea, Dan Ionuț; Streba, Costin Teodor; Vere, Cristin Constantin; Șerbănescu, Mircea; Pirici, Daniel; Comănescu, Maria; Streba, Letiția Adela Maria; Ciurea, Marius Eugen; Mogoantă, Stelian; Rogoveanu, Ion
2014-01-01
Background and Aims. Hepatocellular carcinoma (HCC) remains a leading cause of death by cancer worldwide. Computerized diagnosis systems relying on novel imaging markers gained significant importance in recent years. Our aim was to integrate a novel morphometric measurement—the fractal dimension (FD)—into an artificial neural network (ANN) designed to diagnose HCC. Material and Methods. The study included 21 HCC and 28 liver metastases (LM) patients scheduled for surgery. We performed hematoxylin staining for cell nuclei and CD31/34 immunostaining for vascular elements. We captured digital images and used an in-house application to segment elements of interest; FDs were calculated and fed to an ANN which classified them as malignant or benign, further identifying HCC and LM cases. Results. User intervention corrected segmentation errors and fractal dimensions were calculated. ANNs correctly classified 947/1050 HCC images (90.2%), 1021/1050 normal tissue images (97.23%), 1215/1400 LM (86.78%), and 1372/1400 normal tissues (98%). We obtained excellent interobserver agreement between human operators and the system. Conclusion. We successfully implemented FD as a morphometric marker in a decision system, an ensemble of ANNs designed to differentiate histological images of normal parenchyma from malignancy and classify HCCs and LMs. PMID:25025042
Estimate for the fractal dimension of the Apollonian gasket in d dimensions.
Farr, R S; Griffiths, E
2010-06-01
We adapt a recent theory for the random close packing of polydisperse spheres in three dimensions [R. S. Farr and R. D. Groot, J. Chem. Phys. 131, 244104 (2009)] in order to predict the Hausdorff dimension dA of the Apollonian gasket in dimensions 2 and above. Our approximate results agree with published values in two and three dimensions to within 0.05% and 0.6%, respectively, and we provide predictions for dimensions 4-8. PMID:20866417
NASA Astrophysics Data System (ADS)
Alonso, C.; Benito, R. M.; Tarquis, A. M.
2012-04-01
such complexities from remote sensing images and will applied in this study to see the scaling behavior for each sensor in generalized fractal dimensions. The studied area is located in the provinces of Caceres and Salamanca (east of Iberia Peninsula) with an extension of 32 x 32 km2. The altitude in the area varies from 1,560 to 320 m, comprising natural vegetation in the mountain area (forest and bushes) and agricultural crops in the valleys. Scaling analysis were applied to Landsat-5 and MODIS TERRA to the normalized derived vegetation index (NDVI) on the same region with one day of difference, 13 and 12 of July 2003 respectively. From these images the area of interest was selected obtaining 1024 x 1024 pixels for Landsat image and 128 x 128 pixels for MODIS image. This implies that the resolution for MODIS is 250x250 m. and for Landsat is 30x30 m. From the reflectance data obtained from NIR and RED bands, NDVI was calculated for each image focusing this study on 0.2 to 0.5 ranges of values. Once that both NDVI fields were obtained several fractal dimensions were estimated in each one segmenting the values in 0.20-0.25, 0.25-0.30 and so on to rich 0.45-0.50. In all the scaling analysis the scale size length was expressed in meters, and not in pixels, to make the comparison between both sensors possible. Results are discussed. Acknowledgements This work has been supported by the Spanish MEC under Projects No. AGL2010-21501/AGR, MTM2009-14621 and i-MATH No. CSD2006-00032
NASA Astrophysics Data System (ADS)
Kikuchi, Tsuneo; Nakazawa, Toshihiro; Furukawa, Tetsuo; Higuchi, Toshiyuki; Maruyama, Yukio; Sato, Sojun
1995-05-01
This paper describes the quantitative measurement of the amount of fibrosis in the rat liver using the fractal dimension of the shape of power spectrum. The shape of the power spectrum of the scattered echo from biotissues is strongly affected by its internal structure. The fractal dimension, which is one of the important parameters of the fractal theory, is useful to express the complexity of shape of figures such as the power spectrum. From in vitro experiments using rat liver, it was found that this method can be used to quantitatively measure the amount of fibrosis in the liver, and has the possibility for use in the diagnosis of human liver cirrhosis.
NASA Astrophysics Data System (ADS)
Ul'yanov, A. S.; Lyapina, A. M.; Ulianova, O. V.; Fedorova, V. A.; Uianov, S. S.
2011-04-01
Specific statistical characteristics of biospeckles, emerging under the diffraction of coherent beams on the bacterial colonies, are studied. The dependence of the fractal dimensions of biospeckles on the conditions of both illumination and growth of the colonies is studied theoretically and experimentally. Particular attention is paid to the fractal properties of biospeckles, emerging under the scattering of light by the colonies of the vaccinal strain of the plague microbe. The possibility in principle to classify the colonies of Yersinia pestis EV NIIEG using the fractal dimension analysis is demonstrated.
Ul'yanov, A S; Lyapina, A M; Ulianova, O V; Fedorova, V A; Uianov, S S
2011-04-30
Specific statistical characteristics of biospeckles, emerging under the diffraction of coherent beams on the bacterial colonies, are studied. The dependence of the fractal dimensions of biospeckles on the conditions of both illumination and growth of the colonies is studied theoretically and experimentally. Particular attention is paid to the fractal properties of biospeckles, emerging under the scattering of light by the colonies of the vaccinal strain of the plague microbe. The possibility in principle to classify the colonies of Yersinia pestis EV NIIEG using the fractal dimension analysis is demonstrated. (optical technologies in biophysics and medicine)
Fractal dimension of chromatin: potential molecular diagnostic applications for cancer prognosis
Metze, Konradin
2013-01-01
Fractal characteristics of chromatin, revealed by light or electron microscopy, have been reported during the last 20 years. Fractal features can easily be estimated in digitalized microscopic images and are helpful for diagnosis and prognosis of neoplasias. During carcinogenesis and tumor progression, an increase of the fractal dimension (FD) of stained nuclei has been shown in intraepithelial lesions of the uterine cervix and the anus, oral squamous cell carcinomas or adenocarcinomas of the pancreas. Furthermore, an increased FD of chromatin is an unfavorable prognostic factor in squamous cell carcinomas of the oral cavity and the larynx, melanomas and multiple myelomas. High goodness-of-fit of the regression line of the FD is a favorable prognostic factor in acute leukemias and multiple myelomas. The nucleus has fractal and power-law organization in several different levels, which might in part be interrelated. Some possible relations between modifications of the chromatin organization during carcinogenesis and tumor progression and an increase of the FD of stained chromatin are suggested. Furthermore, increased complexity of the chromatin structure, loss of heterochromatin and a less-perfect self-organization of the nucleus in aggressive neoplasias are discussed. PMID:24063399
Modified box dimension and average weighted receiving time on the weighted fractal networks
Dai, Meifeng; Sun, Yanqiu; Shao, Shuxiang; Xi, Lifeng; Su, Weiyi
2015-01-01
In this paper a family of weighted fractal networks, in which the weights of edges have been assigned to different values with certain scale, are studied. For the case of the weighted fractal networks the definition of modified box dimension is introduced, and a rigorous proof for its existence is given. Then, the modified box dimension depending on the weighted factor and the number of copies is deduced. Assuming that the walker, at each step, starting from its current node, moves uniformly to any of its nearest neighbors. The weighted time for two adjacency nodes is the weight connecting the two nodes. Then the average weighted receiving time (AWRT) is a corresponding definition. The obtained remarkable result displays that in the large network, when the weight factor is larger than the number of copies, the AWRT grows as a power law function of the network order with the exponent, being the reciprocal of modified box dimension. This result shows that the efficiency of the trapping process depends on the modified box dimension: the larger the value of modified box dimension, the more efficient the trapping process is. PMID:26666355
Huang, F.; Peng, R. D.; Liu, Y. H.; Chen, Z. Y.; Ye, M. F.; Wang, L.
2012-09-15
Fractal dust grains of different shapes are observed in a radially confined magnetized radio frequency plasma. The fractal dimensions of the dust structures in two-dimensional (2D) horizontal dust layers are calculated, and their evolution in the dust growth process is investigated. It is found that as the dust grains grow the fractal dimension of the dust structure decreases. In addition, the fractal dimension of the center region is larger than that of the entire region in the 2D dust layer. In the initial growth stage, the small dust particulates at a high number density in a 2D layer tend to fill space as a normal surface with fractal dimension D = 2. The mechanism of the formation of fractal dust grains is discussed.
Nuclear Fractal Dimensions as a Tool for Prognostication of Oral Squamous Cell Carcinoma
Yinti, Shanmukha Raviteja; Boaz, Karen; Lewis, Amitha J; Ashokkumar, Pandya Jay; Kapila, Supriya Nikita
2015-01-01
Background Carcinogenesis follows complex molecular alterations, which are triggered by subtle chromatin architectural changes that are imperceptible to the human eye. As the treatment decisions in Oral Squamous Cell Carcinoma (OSCC) are hindered by the imprecise clinical stage determination and inter-observer variability in histological grading, focus in recent years has shifted to discovering identifiers related to neoplastic cell morphology studied through computer-aided image analysis. One such approach is the assessment of fractal geometry, a technique first described by Mandelbrot, which aids in precise assessment of architecture of natural objects. Assessment and quantification of degree of complexity of these fractal objects (self-similarities in structural complexity at different magnifying scales) is described as fractal dimension (FD). Aim To evaluate the nuclear fractal dimension (NFD) in OSCC using computer-aided image analysis. Materials and Methods Histological sections of 14 selected cases of Oral Squamous Cell Carcinoma (OSCC) and 6 samples of normal buccal mucosa (as control) were stained with Haematoxylin-Eosin and Feulgen stain for histopathological examination and evaluation of nuclear complexity respectively. Fifteen HPF at Invasive Tumour Front (ITF) and Tumour Proper (TP) of Feulgen-stained sections were selected and photographed in test and control samples. At ITF, TP and normal buccal mucosa 200 nuclei each were selected and analyzed using Image J software to quantify FD. The test and control groups were compared statistically using Independent sample t-test and One-way ANOVA. Results Nuclear FD increased progressively towards worst tumour staging as compared to normal buccal mucosa. Conclusion Nuclear FD can be considered for quantification of nuclear architectural changes as a prognostic indicator in OSCC. PMID:26674013
THE FRACTAL DIMENSION OF STAR-FORMING REGIONS AT DIFFERENT SPATIAL SCALES IN M33
Sanchez, Nestor; Alfaro, Emilio J.; Anez, Neyda; Odekon, Mary Crone
2010-09-01
We study the distribution of stars, H II regions, molecular gas, and individual giant molecular clouds in M33 over a wide range of spatial scales. The clustering strength of these components is systematically estimated through the fractal dimension. We find scale-free behavior at small spatial scales and a transition to a larger correlation dimension (consistent with a nearly uniform distribution) at larger scales. The transition region lies in the range {approx}500-1000 pc. This transition defines a characteristic size that separates the regime of small-scale turbulent motion from that of large-scale galactic dynamics. At small spatial scales, bright young stars and molecular gas are distributed with nearly the same three-dimensional fractal dimension (D {sub f,3D} {approx}< 1.9), whereas fainter stars and H II regions exhibit higher values, D {sub f,3D} {approx_equal} 2.2-2.5. Our results indicate that the interstellar medium in M33 is on average more fragmented and irregular than in the Milky Way.
Fractal dimension analysis of landscape scale variability in greenhouse gas production potentials
NASA Astrophysics Data System (ADS)
da Silva Bicalho, Elton; Spokas, Kurt; La Scala, Newton, Jr.
2015-04-01
Soil greenhouse gas emission is influenced by tillage and management practices that modify soil attributes directly related to the dynamics of soil carbon in the agricultural environment. The aim of this study was to assess the soil CO2 and N2O production potentials and their spatial variability characterized by fractal dimension in different scales, in addition to their correlation with other soil attributes. The quantification of soil CO2 and N2O production was carried out from dry soil samples collected in a grid of 50 × 50 m containing 133 points arranged symmetrically on a sugarcane area under green residue management in southern Brazil. Laboratory incubations were used to analyze greenhouse gas dynamics by gas chromatography. Soil CO2 and N2O production were correlated significantly (P < 0.05) with microbial biomass, silt and clay content, pH, available phosphorus, sum of metal cations (bases), and cation exchange capacity. Similarly, these soil attributes also were correlated with microbial biomass, supporting their role in soil microbial activity and greenhouse gas production. Furthermore, variations in the fractal dimension over the scale indicate that the pattern of the spatial variability structure of soil CO2 production potential was correlated to that observed for microbial biomass, pH, available phosphorus, sum of bases, and cation exchange capacity. On the other hand, only the spatial structure of the clay content, pH and the sum of bases were correlated with the soil N2O production. Therefore, examining the fractal dimension enables the spatially visualization of altering processes across a landscape at different scales, which highlights properties that influence greenhouse gas production and emission in agricultural areas.
ERIC Educational Resources Information Center
McCartney, M.; Myers, D.; Sun, Y.
2008-01-01
The divider dimensions of a range of maps of Ireland dating from 1567 to 1893 are evaluated, and it is shown that for maps produced before 1650 the fractal dimension of the map can be correlated to its date of publication. Various classroom uses and extensions are discussed. (Contains 2 figures.)
NASA Astrophysics Data System (ADS)
Ahammer, Helmut; DeVaney, Trevor T. J.
2004-03-01
The boundary of a fractal object, represented in a two-dimensional space, is theoretically a line with an infinitely small width. In digital images this boundary or contour is limited to the pixel resolution of the image and the width of the line commonly depends on the edge detection algorithm used. The Minkowski dimension was evaluated by using three different edge detection algorithms (Sobel, Roberts, and Laplace operator). These three operators were investigated because they are very widely used and because their edge detection result is very distinct concerning the line width. Very common fractals (Sierpinski carpet and Koch islands) were investigated as well as the binary images from a cancer invasion assay taken with a confocal laser scanning microscope. The fractal dimension is directly proportional to the width of the contour line and the fact, that in practice very often the investigated objects are fractals only within a limited resolution range is considered too.
Power spectrum and fractal dimension of laser backscattering from the ocean.
Churnside, James H; Wilson, James J
2006-11-01
We flew an airborne lidar perpendicular to the coastline along straight-line transects that varied in length between 230 and 280 km. The sample spacing was approximately 3 m, so we sampled almost five decades of spatial scales. Except for the return from right at the surface, the power spectra of backscattered power had a power-law dependence on spatial frequency, with a slope of approximately 1.49. This corresponds to a fractal dimension of 1.76. This implies that the distribution is not as patchy as that of a purely turbulent process. PMID:17047710
Measuring capital market efficiency: long-term memory, fractal dimension and approximate entropy
NASA Astrophysics Data System (ADS)
Kristoufek, Ladislav; Vosvrda, Miloslav
2014-07-01
We utilize long-term memory, fractal dimension and approximate entropy as input variables for the Efficiency Index [L. Kristoufek, M. Vosvrda, Physica A 392, 184 (2013)]. This way, we are able to comment on stock market efficiency after controlling for different types of inefficiencies. Applying the methodology on 38 stock market indices across the world, we find that the most efficient markets are situated in the Eurozone (the Netherlands, France and Germany) and the least efficient ones in the Latin America (Venezuela and Chile).
A Brief Historical Introduction to Fractals and Fractal Geometry
ERIC Educational Resources Information Center
Debnath, Lokenath
2006-01-01
This paper deals with a brief historical introduction to fractals, fractal dimension and fractal geometry. Many fractals including the Cantor fractal, the Koch fractal, the Minkowski fractal, the Mandelbrot and Given fractal are described to illustrate self-similar geometrical figures. This is followed by the discovery of dynamical systems and…
NASA Astrophysics Data System (ADS)
Monthus, Cécile
2015-09-01
For Gaussian Spin-Glasses in low dimensions, we introduce a simple Strong Disorder renormalization at zero temperature in order to construct ground states for Periodic and Anti-Periodic boundary conditions. The numerical study in dimensions d = 2 (up to sizes 20482) and d = 3 (up to sizes 1283) yields that Domain Walls are fractal of dimensions ds(d = 2) ≃ 1.27 and ds(d = 3) ≃ 2.55, respectively.
Taylor, Adele M.; MacGillivray, Thomas J.; Henderson, Ross D.; Ilzina, Lasma; Dhillon, Baljean; Starr, John M.; Deary, Ian J.
2015-01-01
Purpose Cerebral microvascular disease is associated with dementia. Differences in the topography of the retinal vascular network may be a marker for cerebrovascular disease. The association between cerebral microvascular state and non-pathological cognitive ageing is less clear, particularly because studies are rarely able to adjust for pre-morbid cognitive ability level. We measured retinal vascular fractal dimension (Df) as a potential marker of cerebral microvascular disease. We examined the extent to which it contributes to differences in non-pathological cognitive ability in old age, after adjusting for childhood mental ability. Methods Participants from the Lothian Birth Cohort 1936 Study (LBC1936) had cognitive ability assessments and retinal photographs taken of both eyes aged around 73 years (n = 648). IQ scores were available from childhood. Retinal vascular Df was calculated with monofractal and multifractal analysis, performed on custom-written software. Multiple regression models were applied to determine associations between retinal vascular Df and general cognitive ability (g), processing speed, and memory. Results Only three out of 24 comparisons (two eyes × four Df parameters × three cognitive measures) were found to be significant. This is little more than would be expected by chance. No single association was verified by an equivalent association in the contralateral eye. Conclusions The results show little evidence that fractal measures of retinal vascular differences are associated with non-pathological cognitive ageing. PMID:25816017
NASA Technical Reports Server (NTRS)
Bazell, David; Dwek, Eli
1990-01-01
Mathis and Whiffen (1989) have recently suggested that interstellar dust particles are fluffy aggregates of submicron-size particles composed of various astronomical minerals. These dust particles should exhibit optical properties that are quite different from standard dust, characterized by spherical particles of various homogeneous mineral composition. In this paper, the discrete dipole approximation (DDA) method is used to examine the effects of chemical inhomogeneities and spatial structure on the optical properties of interstellar Mathis-Whiffen-type dust particles. The spatial structure of the dust is represented by its fractal dimension, and the chemical inhomogeneities are simulated by randomly assigning the composition of the occupied sites in the structure to be either carbon or silicate. It is found that compositional inhomogeneities are the dominant parameter affecting the shape of the 9.7 and 18 micron silicate bands. Some bands-shape variations can be attributed to the fractal dimension of the dust. The results derived here can be used to explain or constrain variations in these parameters among various astronomical objects.
NASA Astrophysics Data System (ADS)
Inclan, Rosa Maria
2016-04-01
Knowledge on three dimensional soil pore architecture is important to improve our understanding of the factors that control a number of critical soil processes as it controls biological, chemical and physical processes at various scales. Computed Tomography (CT) images provide increasingly reliable information about the geometry of pores and solids in soils at very small scale with the benefit that is a non-invasive technique. Fractal formalism has revealed as a useful tool in these cases where highly complex and heterogeneous meda are studied. One of these quantifications is mass dimension (Dm) and spectral dimension (d) applied to describe the water and gas diffusion coefficients in soils (Tarquis et al., 2012). In this work, intact soil samples were collected from the first three horizons of La Herreria soil. This station is located in the lowland mountain area of Sierra de Guadarrama (Santolaria et al., 2015) and it represents a highly degraded type of site as a result of the livestock keeping. The 3D images, of 45.1 micro-m resolution (256x256x256 voxels), were obtained and then binarized following the singularity-CA method (Martín-Sotoca et al. 2016). Based on these images Dm and d were estimated. The results showed an statistical difference in porosity, Dm and d for each horizon. This fact has a direct implication in diffusion parameters for a pore network modeling based on both fractal dimensions. These soil parameters will constitute a basis for site characterization for further studies regarding soil degradation; determining the interaction between soil, plant and atmosphere with respect to human induced activities as well as the basis for several nitrogen and carbon cycles modeling. References Martin Sotoca; J.J. Ana M. Tarquis, Antonio Saa Requejo, and Juan B. Grau (2016). Pore detection in Computed Tomography (CT) soil 3D images using singularity map analysis. Geophysical Research Abstracts, 18, EGU2016-829. Santolaria-Canales, Edmundo and the Gu
NASA Astrophysics Data System (ADS)
Bayrak, Yusuf; Bayrak, Erdem
2012-09-01
We investigated the regional variations of Gutenberg-Richter (G-R) parameters (a and b) and fractal (correlation) dimension (DC) and relations among these parameters for the different regions in Western Anatolia (WA). The whole examined area (26-33°E, 33-40.5°N) is divided into 15 different seismogenic regions based on their tectonic and seismotectonic regimes. We used database including 69,182 earthquakes for the instrumental period from 1900 to 2011. We calculated b value, which is the slope of the frequency-magnitude Gutenberg-Richter relationship, from maximum likelihood method (ML) and DC value, which is the slope of log10C(r) versus log10r, from correlation integral using the least-squares (LS) method. Computed values for 15 different seismogenic regions are mapped using different color scale for different range of values of b and DC. Regional distributions of these parameters reveal information about regional variation of stress level and geological complexity. We concluded Aegean arc and Aegean islands, Aliağa fault and Büyük Menderes Graben the most vulnerable regions for occurrence of the large earthquakes in WA considering the computed lowest b-values and the highest DC-values in these regions. Since DC/b values are the highest in these regions, this ratio may be used as an indicator of earthquake hazard levels of different seismogenic zones in a studied region. An effort is made to find relationships between the G-R parameters and fractal dimension. We observed negative correlation between DC and b values and positive correlation between DC and a/b values for different regions of WA. We observed that the relationship between a/b and DC can be used for seismicity, earthquake risk and hazard studies because of the computed high correlation coefficient and fewer scattering of these parameters.
NASA Astrophysics Data System (ADS)
Raupov, Dmitry S.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Kornilin, Dmitry V.; Zakharov, Valery P.; Khramov, Alexander G.
2016-04-01
Optical coherence tomography (OCT) is usually employed for the measurement of tumor topology, which reflects structural changes of a tissue. We investigated the possibility of OCT in detecting changes using a computer texture analysis method based on Haralick texture features, fractal dimension and the complex directional field method from different tissues. These features were used to identify special spatial characteristics, which differ healthy tissue from various skin cancers in cross-section OCT images (B-scans). Speckle reduction is an important pre-processing stage for OCT image processing. In this paper, an interval type-II fuzzy anisotropic diffusion algorithm for speckle noise reduction in OCT images was used. The Haralick texture feature set includes contrast, correlation, energy, and homogeneity evaluated in different directions. A box-counting method is applied to compute fractal dimension of investigated tissues. Additionally, we used the complex directional field calculated by the local gradient methodology to increase of the assessment quality of the diagnosis method. The complex directional field (as well as the "classical" directional field) can help describe an image as set of directions. Considering to a fact that malignant tissue grows anisotropically, some principal grooves may be observed on dermoscopic images, which mean possible existence of principal directions on OCT images. Our results suggest that described texture features may provide useful information to differentiate pathological from healthy patients. The problem of recognition melanoma from nevi is decided in this work due to the big quantity of experimental data (143 OCT-images include tumors as Basal Cell Carcinoma (BCC), Malignant Melanoma (MM) and Nevi). We have sensitivity about 90% and specificity about 85%. Further research is warranted to determine how this approach may be used to select the regions of interest automatically.
Pore size distribution in porous glass: fractal dimension obtained by calorimetry
NASA Astrophysics Data System (ADS)
Neffati, R.; Rault, J.
2001-05-01
By differential Scanning Calorimetry (DSC), at low heating rate and using a technique of fractionation, we have measured the equilibrium DSC signal (heat flow) J q 0 of two families of porous glass saturated with water. The shape of the DSC peak obtained by these techniques is dependent on the sizes distribution of the pores. For porous glass with large pore size distribution, obtained by sol-gel technology, we show that in the domain of ice melting, the heat flow Jq is related to the melting temperature depression of the solvent, Δ T m , by the scaling law: J q 0˜Δ T m - (1 + D). We suggest that the exponent D is of the order of the fractal dimension of the backbone of the pore network and we discuss the influence of the variation of the melting enthalpy with the temperature on the value of this exponent. Similar D values were obtained from small angle neutron scattering and electronic energy transfer measurements on similar porous glass. The proposed scaling law is explained if one assumes that the pore size distribution is self similar. In porous glass obtained from mesomorphic copolymers, the pore size distribution is very sharp and therefore this law is not observed. One concludes that DSC, at low heating rate ( q? 2°C/min) is the most rapid and less expensive method for determining the pore distribution and the fractal exponent of a porous material.
Fractal Feature Analysis Of Beef Marblingpatterns
NASA Astrophysics Data System (ADS)
Chen, Kunjie; Qin, Chunfang
The purpose of this study is to investigate fractal behavior of beef marbling patterns and to explore relationships between fractal dimensions and marbling scores. Authors firstly extracted marbling images from beef rib-eye crosssection images using computer image processing technologies and then implemented the fractal analysis on these marbling images based on the pixel covering method. Finally box-counting fractal dimension (BFD) and informational fractal dimension (IFD) of one hundred and thirty-five beef marbling images were calculated and plotted against the beef marbling scores. The results showed that all beef marbling images exhibit fractal behavior over the limited range of scales accessible to analysis. Furthermore, their BFD and IFD are closely related to the score of beef marbling, suggesting that fractal analyses can provide us a potential tool to calibrate the score of beef marbling.
Fractal Structure in Human Cerebellum Measured by MRI
NASA Astrophysics Data System (ADS)
Zhang, Luduan; Yue, Guang; Brown, Robert; Liu, Jingzhi
2003-10-01
Fractal dimension has been used to quantify the structures of a wide range of objects in biology and medicine. We measured fractal dimension of human cerebellum (CB) in magnetic resonance images of 24 healthy young subjects (12 men, 12 women). CB images were resampled to a series of image sets with different three-dimensional resolutions. At each resolution, the skeleton of the CB white matter was obtained and the number of pixels belonging to the skeleton was determined. Fractal dimension of the CB skeleton was calculated using the box-counting method. The results indicated that the CB skeleton is a highly fractal structure, with a fractal dimension of 2.57+/-0.01. No significant difference in the CB fractal dimension was observed between men and women. Fractal dimension may serve as a quantitative index for structural complexity of the CB at its developmental, degenerative, or evolutionary stages.
Topological Vulnerability Evaluation Model Based on Fractal Dimension of Complex Networks.
Gou, Li; Wei, Bo; Sadiq, Rehan; Sadiq, Yong; Deng, Yong
2016-01-01
With an increasing emphasis on network security, much more attentions have been attracted to the vulnerability of complex networks. In this paper, the fractal dimension, which can reflect space-filling capacity of networks, is redefined as the origin moment of the edge betweenness to obtain a more reasonable evaluation of vulnerability. The proposed model combining multiple evaluation indexes not only overcomes the shortage of average edge betweenness's failing to evaluate vulnerability of some special networks, but also characterizes the topological structure and highlights the space-filling capacity of networks. The applications to six US airline networks illustrate the practicality and effectiveness of our proposed method, and the comparisons with three other commonly used methods further validate the superiority of our proposed method. PMID:26751371
Topological Vulnerability Evaluation Model Based on Fractal Dimension of Complex Networks
Gou, Li; Wei, Bo; Sadiq, Rehan; Sadiq, Yong; Deng, Yong
2016-01-01
With an increasing emphasis on network security, much more attentions have been attracted to the vulnerability of complex networks. In this paper, the fractal dimension, which can reflect space-filling capacity of networks, is redefined as the origin moment of the edge betweenness to obtain a more reasonable evaluation of vulnerability. The proposed model combining multiple evaluation indexes not only overcomes the shortage of average edge betweenness’s failing to evaluate vulnerability of some special networks, but also characterizes the topological structure and highlights the space-filling capacity of networks. The applications to six US airline networks illustrate the practicality and effectiveness of our proposed method, and the comparisons with three other commonly used methods further validate the superiority of our proposed method. PMID:26751371
NASA Astrophysics Data System (ADS)
Braga, F. L.; Mattos, O. A.; Amorin, V. S.; Souza, A. B.
2015-07-01
Clusters formation models have been extensively studied in literature, and one of the main task of this research area is the analysis of the particle aggregation processes. Some work support that the main characteristics of this processes are strictly correlated to the cluster morphology, for example in DLA. It is expected that in the DLA clusters formation with particles containing different sizes the modification of the aggregation processes can be responsible for changes in the DLA morphology. The present article is going to analyze the formation of DLA clusters of particles with different sizes and show that the aggregates obtained by this approach generate an angle selection mechanism on dendritic growth that influences the shielding effect of the DLA edge and affect the fractal dimension of the clusters.
2013-01-01
Background Prostate cancer is a serious public health problem that affects quality of life and has a significant mortality rate. The aim of the present study was to quantify the fractal dimension and Shannon’s entropy in the histological diagnosis of prostate cancer. Methods Thirty-four patients with prostate cancer aged 50 to 75 years having been submitted to radical prostatectomy participated in the study. Histological slides of normal (N), hyperplastic (H) and tumor (T) areas of the prostate were digitally photographed with three different magnifications (40x, 100x and 400x) and analyzed. The fractal dimension (FD), Shannon’s entropy (SE) and number of cell nuclei (NCN) in these areas were compared. Results FD analysis demonstrated the following significant differences between groups: T vs. N and H vs. N groups (p < 0.05) at a magnification of 40x; T vs. N (p < 0.01) at 100x and H vs. N (p < 0.01) at 400x. SE analysis revealed the following significant differences groups: T vs. H and T vs. N (p < 0.05) at 100x; and T vs. H and T vs. N (p < 0.001) at 400x. NCN analysis demonstrated the following significant differences between groups: T vs. H and T vs. N (p < 0.05) at 40x; T vs. H and T vs. N (p < 0.0001) at 100x; and T vs. H and T vs. N (p < 0.01) at 400x. Conclusions The quantification of the FD and SE, together with the number of cell nuclei, has potential clinical applications in the histological diagnosis of prostate cancer. PMID:23414368
Entanglement entropy on fractals
NASA Astrophysics Data System (ADS)
Faraji Astaneh, Amin
2016-03-01
We use the heat kernel method to calculate the entanglement entropy for a given entangling region on a fractal. The leading divergent term of the entropy is obtained as a function of the fractal dimension as well as the walk dimension. The power of the UV cutoff parameter is (generally) a fractional number, which, indeed, is a certain combination of these two indices. This exponent is known as the spectral dimension. We show that there is a novel log-periodic oscillatory behavior in the expression of entropy which has root in the complex dimension of the fractal. We finally indicate that the holographic calculation in a certain hyperscaling-violating bulk geometry yields the same leading term for the entanglement entropy, if one identifies the effective dimension of the hyperscaling-violating theory with the spectral dimension of the fractal. We provide additional support by comparing the behavior of the thermal entropy in terms of the temperature, computed for two geometries, the fractal geometry and the hyperscaling-violating background.
Determination of the fractal dimension for the epitaxial n-GaAs surface in the local limit
Torkhov, N. A. Bozhkova, V. G.; Ivonin, I. V.; Novikov, V. A.
2009-01-15
Atomic-force microscopy studies of epitaxial n-GaAs surfaces prepared to deposit barrier contacts showed that major relief for such surfaces is characterized by a roughness within 3-15 nm, although 'surges' up to 30-70 nm are observed. Using three independent methods for determining the spatial dimension of the surface, based on the fractal analysis for the surface (triangulation method), its section contours in the horizontal plane, and the vertical section (surface profile), it was shown that the active surface for epitaxial n-GaAs obeys all main features of behavior for fractal Brownian surfaces and, in the local approximation, can be characterized by the fractal dimension D{sub f} slightly differing for various measuring scales. The most accurate triangulation method showed that the fractal dimensions for the studied surface of epitaxial n-GaAs for measurement scales from 0.692 to 0.0186 {mu}m are in the range D{sub f} = 2.490-2.664. The real surface area S{sub real} for n-GaAs epitaxial layers was estimated using a graphical method in the approximation {delta} {sup {yields}} 0 {delta} is the measurement scale parameter). It was shown that the real surface area for epitaxial n-GaAs can significantly (ten times and more) exceed the area of the visible contact window.
NASA Technical Reports Server (NTRS)
Garneau, S.; Plaut, J. J.
2000-01-01
The surface roughness of the Vastitas Borealis Formation on Mars was analyzed with fractal statistics. Root mean square slopes and fractal dimensions were calculated for 74 topographic profiles. Results have implications for radar scattering models.
NASA Astrophysics Data System (ADS)
Karemore, Gopal; Nielsen, Mads
2009-02-01
Structural texture measures are used to address the aspect of breast cancer risk assessment in screening mammograms. The current study investigates whether texture properties characterized by local Fractal Dimension (FD) and Lacunarity contribute to asses breast cancer risk. FD represents the complexity while the Lacunarity characterize the gappiness of a fractal. Our cross-sectional case-control study includes mammograms of 50 patients diagnosed with breast cancer in the subsequent 2-4 years and 50 matched controls. The longitudinal double blind placebo controlled HRT study includes 39 placebo and 36 HRT treated volunteers for two years. ROIs with same dimension (250*150 pixels) were created behind the nipple region on these radiographs. Box counting method was used to calculate the fractal dimension (FD) and the Lacunarity. Paired t-test and Pearson correlation coefficient were calculated. It was found that there were no differences between cancer and control group for FD (P=0.8) and Lacunarity (P=0.8) in crosssectional study whereas earlier published heterogeneity examination of radiographs (BC-HER) breast cancer risk score separated groups (p=0.002). In the longitudinal study, FD decreased significantly (P<0.05) in the HRT treated population while Lacunarity remained insignificant (P=0.2). FD is negatively correlated to Lacunarity (-0.74, P<0.001), BIRADS (-0.34, P<0.001) and Percentage Density (-0.41, P<0.001). FD is invariant to the mammographic texture change from control to cancer population but marginally varying in HRT treated population. This study yields no evidence that lacunarity or FD are suitable surrogate markers of mammographic heterogeneity as they neither pick up breast cancer risk, nor show good sensitivity to HRT.
NASA Astrophysics Data System (ADS)
Rodkin, M. V.; Shatakhtsyan, A. R.
2015-05-01
The method for calculating the fractal correlation dimension is applied for analyzing the data on the locations of large and extralarge ore deposits. The approach implemented in this study differs by a few of important points from that commonly used, e.g., in the calculations of the correlation dimension for a set of the epicenters (hypocenters) of the earthquakes. Firstly, we demonstrate the possibility and advisability of obtaining different dimension estimates for different spatial scales. Such a separation turned out to be useful in distinguishing between the regularities in the location of ore deposits on the scale of an ore cluster, ore province, and entire continent. Secondly, we introduce a new notion, a mixed correlation dimension, and use it for different types of the objects (e.g., Au and Ag). The standard formula for calculating the correlation dimension is trivially generalized on this case. It is shown that the values of the correlation dimension can be lower and higher than the dimension of the hosting medium. The cases when the correlation dimension is higher than that of the hosting medium are interpreted as a "mutual repulsion" of the deposits of the two mentioned types. In contrast, the small correlation dimensions indicate that the deposits of the corresponding types tend to have spatially close locations. The calculations are conducted for the spherical Earth. The method is applied to the data on the large and extralarge world-class ore deposits from the Largest Mineral Deposits of the World (LMDs) geoinformation system (GIS). Different patterns of the studied behavior are illustrated by the model examples.
Fractal dimensions of wave functions and local spectral measures on the Fibonacci chain
NASA Astrophysics Data System (ADS)
Macé, Nicolas; Jagannathan, Anuradha; Piéchon, Frédéric
2016-05-01
We present a theoretical framework for understanding the wave functions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong modulation of the hopping amplitudes, are in good agreement with published numerical data. In the perturbative limit, we show a symmetry of wave functions under permutation of site and energy indices. We compute the wave-function renormalization factors and from them deduce analytical expressions for the fractal exponents corresponding to individual wave functions, as well as their global averages. The multifractality of wave functions is seen to appear at next-to-leading order in ρ . Exponents for the local spectral density are given, in extremely good accord with numerical calculations. Interestingly, our analytical results for exponents are observed to describe the system rather well even for values of ρ well outside the domain of applicability of perturbation theory.
Li, Qiaowei; Yuan, Yin; Gao, Zhonghai; Chen, Falin
2014-01-01
Background This study aimed to investigate the correlation between quantitative retinal vascular parameters such as central retinal arteriolar equivalent (CRAE) and retinal vascular fractal dimension (D(f)), and cardiovascular risk factors in the Chinese Han population residing in the in islands of southeast China. Methodology/Principle Findings In this cross-sectional study, fundus photographs were collected and semi-automated analysis software was used to analyze retinal vessel diameters and fractal dimensions. Cardiovascular risk factors such as relevant medical history, blood pressure (BP), lipids, and blood glucose data were collected. Subjects had a mean age of 51.9±12.0 years and included 812 (37.4%) males and 1,357 (62.6%) females. Of the subjects, 726 (33.5%) were overweight, 226 (10.4%) were obese, 272 (12.5%) had diabetes, 738 (34.0%) had hypertension, and 1,156 (53.3%) had metabolic syndrome. After controlling for the effects of potential confounders, multivariate analyses found that age (β = 0.06, P = 0.008), sex (β = 1.33, P = 0.015), mean arterial blood pressure (β = −0.12, P<0.001), high-sensitivity C-reactive protein (β = −0.22, P = 0.008), and CRVE (β = 0.23, P<0.001) were significantly associated with CRAE. Age (β = −0.0012, P<0.001), BP classification (prehypertension: β = −0.0075, P = 0.014; hypertension: β = −0.0131, P = 0.002), and hypertension history (β = −0.0007, P = 0.009) were significantly associated with D(f). Conclusions/Significance D(f) exhibits a stronger association with BP than CRAE. Thus, D(f) may become a useful indicator of cardiovascular risk. PMID:25188273
Small-angle scattering from fat fractals
NASA Astrophysics Data System (ADS)
Anitas, Eugen M.
2014-06-01
A number of experimental small-angle scattering (SAS) data are characterized by a succession of power-law decays with arbitrarily decreasing values of scattering exponents. To describe such data, here we develop a new theoretical model based on 3D fat fractals (sets with fractal structure, but nonzero volume) and show how one can extract structural information about the underlying fractal structure. We calculate analytically the monodisperse and polydisperse SAS intensity (fractal form factor and structure factor) of a newly introduced model of fat fractals and study its properties in momentum space. The system is a 3D deterministic mass fractal built on an extension of the well-known Cantor fractal. The model allows us to explain a succession of power-law decays and respectively, of generalized power-law decays (GPLD; superposition of maxima and minima on a power-law decay) with arbitrarily decreasing scattering exponents in the range from zero to three. We show that within the model, the present analysis allows us to obtain the edges of all the fractal regions in the momentum space, the number of fractal iteration and the fractal dimensions and scaling factors at each structural level in the fractal. We applied our model to calculate an analytical expression for the radius of gyration of the fractal. The obtained quantities characterizing the fat fractal are correlated to variation of scaling factor with the iteration number.
ERIC Educational Resources Information Center
House, Garvey; Zelhart, Paul F.
The complexity (fractal dimension value) of responses to the Rey-Osterrieth Complex Figure Test (ROCFT) between 10 undergraduate students with learning disabilities and a comparison group of 10 students without learning disabilities were compared. The fractal value of responses was assessed under three conditions (copy, immediate, and delay) by…
Assessing severity of obstructive sleep apnea by fractal dimension sequence analysis of sleep EEG
NASA Astrophysics Data System (ADS)
Zhang, J.; Yang, X. C.; Luo, L.; Shao, J.; Zhang, C.; Ma, J.; Wang, G. F.; Liu, Y.; Peng, C.-K.; Fang, J.
2009-10-01
Different sleep stages are associated with distinct dynamical patterns in EEG signals. In this article, we explored the relationship between the sleep architecture and fractal dimension (FD) of sleep EEG. In particular, we applied the FD analysis to the sleep EEG of patients with obstructive sleep apnea-hypopnea syndrome (OSAHS), which is characterized by recurrent oxyhemoglobin desaturation and arousals from sleep, a disease which received increasing public attention due to its significant potential impact on health. We showed that the variation of FD reflects the macrostructure of sleep. Furthermore, the fast fluctuation of FD, as measured by the zero-crossing rate of detrended FD (zDFD), is a useful indicator of sleep disturbance, and therefore, correlates with apnea-hypopnea index (AHI), and hourly number of blood oxygen saturation (SpO 2) decreases greater than 4%, as obstructive apnea/hypopnea disturbs sleep architecture. For practical purpose, a modified index combining zDFD of EEG and body mass index (BMI) may be useful for evaluating the severity of OSAHS symptoms.
Ictal EEG fractal dimension in ECT predicts outcome at 2 weeks in schizophrenia.
Abhishekh, Hulegar A; Thirthalli, Jagadisha; Manjegowda, Anusha; Phutane, Vivek H; Muralidharan, Kesavan; Gangadhar, Bangalore N
2013-09-30
Studies of electroconvulsive therapy (ECT) have found an association between ictal electroencephalographic (EEG) measures and clinical outcome in depression. Such studies are lacking in schizophrenia. Consenting schizophrenia patients receiving ECT were assessed using the Brief Psychiatric Rating Scale (BPRS) before and 2 weeks after the start of ECT. The patients' seizure was monitored using EEG. In 26 patients, completely artifact-free EEG derived from the left frontal-pole (FP1) channel and electrocardiography (ECG) were available. The fractal dimension (FD) was computed to assess 4-s EEG epochs, and the maximal value from the earliest ECT session (2nd, 3rd or 4th) was used for analysis. There was a significant inverse correlation between the maximum FD and the total score following 6th ECT. An inverse Inverse correlation was also observed between the maximum FD and the total number of ECTs administered as well as the maximum heart rate (HR) and BPRS scores following 6th ECT. In patients with schizophrenia greater intensity of seizures (higher FD) during initial sessions of ECT is associated with better response at the end of 2 weeks. PMID:23261182
Medical image retrieval and analysis by Markov random fields and multi-scale fractal dimension.
Backes, André Ricardo; Gerhardinger, Leandro Cavaleri; Batista Neto, João do Espírito Santo; Bruno, Odemir Martinez
2015-02-01
Many Content-based Image Retrieval (CBIR) systems and image analysis tools employ color, shape and texture (in a combined fashion or not) as attributes, or signatures, to retrieve images from databases or to perform image analysis in general. Among these attributes, texture has turned out to be the most relevant, as it allows the identification of a larger number of images of a different nature. This paper introduces a novel signature which can be used for image analysis and retrieval. It combines texture with complexity extracted from objects within the images. The approach consists of a texture segmentation step, modeled as a Markov Random Field process, followed by the estimation of the complexity of each computed region. The complexity is given by a Multi-scale Fractal Dimension. Experiments have been conducted using an MRI database in both pattern recognition and image retrieval contexts. The results show the accuracy of the proposed method in comparison with other traditional texture descriptors and also indicate how the performance changes as the level of complexity is altered. PMID:25586375
Medical image retrieval and analysis by Markov random fields and multi-scale fractal dimension
NASA Astrophysics Data System (ADS)
Backes, André Ricardo; Cavaleri Gerhardinger, Leandro; do Espírito Santo Batista Neto, João; Martinez Bruno, Odemir
2015-02-01
Many Content-based Image Retrieval (CBIR) systems and image analysis tools employ color, shape and texture (in a combined fashion or not) as attributes, or signatures, to retrieve images from databases or to perform image analysis in general. Among these attributes, texture has turned out to be the most relevant, as it allows the identification of a larger number of images of a different nature. This paper introduces a novel signature which can be used for image analysis and retrieval. It combines texture with complexity extracted from objects within the images. The approach consists of a texture segmentation step, modeled as a Markov Random Field process, followed by the estimation of the complexity of each computed region. The complexity is given by a Multi-scale Fractal Dimension. Experiments have been conducted using an MRI database in both pattern recognition and image retrieval contexts. The results show the accuracy of the proposed method in comparison with other traditional texture descriptors and also indicate how the performance changes as the level of complexity is altered.
NASA Astrophysics Data System (ADS)
Fernandes, Maurício Anderson; Ribeiro Rosa, Edvaldo Antônio; Johann, Aline Cristina Batista Rodrigues; Grégio, Ana Maria Trindade; Trevilatto, Paula Cristina; Azevedo-Alanis, Luciana Reis
2016-01-01
Objectives: To test the capacity of the digital tool, fractal dimension (FD) analysis, in identifying subtle differences in bone pattern in patients with renal osteodystrophy (RO), correlated with the time of hemodialysis, in different regions of interest, delineated on panoramic and periapical radiographs. Study design: A total of 34 patients with chronic renal disease undergoing hemodialysis were submitted to panoramic and periapical radiographs. Different regions of interest were delineated on the mandibular body and ramus. FD was analyzed by means of the software program ImageJ and correlated with the time of hemodialysis. Results: The sample consisted of 34 subjects. The time of hemodialysis varied from 1 to 286 months. There was significant correlation between the time of hemodialysis and the FD values in the region delineated in the mandibular angle (r = 0.498; p = 0.003) and this was shown in the periapical radiographs as well (r = -0.349; p = 0.043). Conclusions: FD analysis was a useful tool in detecting alterations caused by RO in bone pattern, in panoramic and periapical radiographs.
Cimolin, Veronica; Galli, Manuela; Rigoldi, Chiara; Grugni, Graziano; Vismara, Luca; de Souza, Shirley Aparecida Fabris; Mainardi, Luca; Albertini, Giorgio; Capodaglio, Paolo
2014-01-01
The suitability of new dynamic system analysis was investigated to compare postural control in Prader-Willi syndrome (PWS) and Down syndrome (DS) patients. Time-domain, frequency-domain parameters and fractal dimension (FD) of centre of pressure (CoP) were computed in maintaining normal standing on a force platform in 20 DS and 13 PWS patients, compared to 26 obese (obese control group, OCG) and 20 healthy individuals (healthy control group, HCG). DS and PWS showed greater displacements along both directions and longer sway path (SP) parameter than HCG and OCG, with statistical differences between PWS and DS for anteroposterior displacement and SP. DS used higher frequency strategy when compared to PWS, OCG and HCG. Both DS and PWS were characterised by greater values of FD than OCG and HCG, with higher values in DS. The analyses in frequency domain and of the dynamic nature of CoP suggest that DS patients are characterised by a more complex and irregular signal than PWS patients. PMID:23360287
Gene Entropy-Fractal Dimension Informatics with Application to Mouse-Human Translational Medicine
Holden, T.; Cheung, E.; Dehipawala, S.; Ye, J.; Tremberger, G.; Lieberman, D.; Cheung, T.
2013-01-01
DNA informatics represented by Shannon entropy and fractal dimension have been used to form 2D maps of related genes in various mammals. The distance between points on these maps for corresponding mRNA sequences in different species is used to study evolution. By quantifying the similarity of genes between species, this distance might be indicated when studies on one species (mouse) would tend to be valid in the other (human). The hypothesis that a small distance from mouse to human could facilitate mouse to human translational medicine success is supported by the studied ESR-1, LMNA, Myc, and RNF4 sequences. ID1 and PLCZ1 have larger separation. The collinearity of displacement vectors is further analyzed with a regression model, and the ID1 result suggests a mouse-chimp-human translational medicine approach. Further inference was found in the tumor suppression gene, p53, with a new hypothesis of including the bovine PKM2 pathways for targeting the glycolysis preference in many types of cancerous cells, consistent with quantum metabolism models. The distance between mRNA and protein coding CDS is proposed as a measure of the pressure associated with noncoding processes. The Y-chromosome DYS14 in fetal micro chimerism that could offer protection from Alzheimer's disease is given as an example. PMID:23586047
Gene entropy-fractal dimension informatics with application to mouse-human translational medicine.
Holden, T; Cheung, E; Dehipawala, S; Ye, J; Tremberger, G; Lieberman, D; Cheung, T
2013-01-01
DNA informatics represented by Shannon entropy and fractal dimension have been used to form 2D maps of related genes in various mammals. The distance between points on these maps for corresponding mRNA sequences in different species is used to study evolution. By quantifying the similarity of genes between species, this distance might be indicated when studies on one species (mouse) would tend to be valid in the other (human). The hypothesis that a small distance from mouse to human could facilitate mouse to human translational medicine success is supported by the studied ESR-1, LMNA, Myc, and RNF4 sequences. ID1 and PLCZ1 have larger separation. The collinearity of displacement vectors is further analyzed with a regression model, and the ID1 result suggests a mouse-chimp-human translational medicine approach. Further inference was found in the tumor suppression gene, p53, with a new hypothesis of including the bovine PKM2 pathways for targeting the glycolysis preference in many types of cancerous cells, consistent with quantum metabolism models. The distance between mRNA and protein coding CDS is proposed as a measure of the pressure associated with noncoding processes. The Y-chromosome DYS14 in fetal micro chimerism that could offer protection from Alzheimer's disease is given as an example. PMID:23586047
Multiscale differential fractal feature with application to target detection
NASA Astrophysics Data System (ADS)
Shi, Zelin; Wei, Ying; Huang, Shabai
2004-07-01
A multiscale differential fractal feature of an image is proposed and a small target detection method from complex nature clutter is presented. Considering the speciality that the fractal features of man-made objects change much more violently than that of nature's when the scale is varied, fractal features at multiple scales used for distinguishing man-made target from nature clutter should have more advantages over standard fractal dimensions. Multiscale differential fractal dimensions are deduced from typical fractal model and standard covering-blanket method is improved and used to estimate multiscale fractal dimensions. A multiscale differential fractal feature is defined as the variation of fractal dimensions between two scales at a rational scale range. It can stand out the fractal feature of man-made object from natural clutters much better than the fractal dimension by standard covering-blanket method. Meanwhile, the calculation and the storage amount are reduced greatly, they are 4/M and 2/M that of the standard covering-blanket method respectively (M is scale). In the image of multiscale differential fractal feature, local gray histogram statistical method is used for target detection. Experiment results indicate that this method is suitable for both kinds background of land and sea. It also can be appropriate in both kinds of infrared and TV images, and can detect small targets from a single frame correctly. This method is with high speed and is easy to be implemented.
Mossotti, Victor G.; Eldeeb, A. Raouf
2000-01-01
Turcotte, 1997, and Barton and La Pointe, 1995, have identified many potential uses for the fractal dimension in physicochemical models of surface properties. The image-analysis program described in this report is an extension of the program set MORPH-I (Mossotti and others, 1998), which provided the fractal analysis of electron-microscope images of pore profiles (Mossotti and Eldeeb, 1992). MORPH-II, an integration of the modified kernel of the program MORPH-I with image calibration and editing facilities, was designed to measure the fractal dimension of the exposed surfaces of stone specimens as imaged in cross section in an electron microscope.
2010-01-01
Background Fractal geometry is employ to characterize the irregular objects and had been used in experimental and clinic applications. Starting from a previous work, here we made a theoretical research based on a geometric generalization of the experimental results, to develop a theoretical generalization of the stenotic and restenotic process, based on fractal geometry and Intrinsic Mathematical Harmony. Methods Starting from all the possibilities of space occupation in box-counting space, all arterial prototypes differentiating normality and disease were obtained with a computational simulation. Measures from 2 normal and 3 re-stenosed arteries were used as spatial limits of the generalization. Results A new methodology in animal experimentation was developed, based on fractal geometric generalization. With this methodology, it was founded that the occupation space possibilities in the stenotic process are finite and that 69,249 arterial prototypes are obtained as a total. Conclusions The Intrinsic Mathematical Harmony reveals a supra-molecular geometric self-organization, where the finite and discrete fractal dimensions of arterial layers evaluate objectively the arterial stenosis and restenosis process. PMID:20846449
Meng, Zhiyong; Hashmi, Sara M; Elimelech, Menachem
2013-02-15
The time-evolutions of nanoparticle hydrodynamic radius and aggregate fractal dimension during the aggregation of fullerene (C(60)) nanoparticles (FNPs) were measured via simultaneous multiangle static and dynamic light scattering. The FNP aggregation behavior was determined as a function of monovalent (NaCl) and divalent (CaCl(2)) electrolyte concentration, and the impact of addition of dissolved natural organic matter (humic acid) to the solution was also investigated. In the absence of humic acid, the fractal dimension decreased over time with monovalent and divalent salts, suggesting that aggregates become slightly more open and less compact as they grow. Although the aggregates become slightly more open, the magnitude of the fractal dimension suggests intermediate aggregation between the diffusion- and reaction-limited regimes. We observed different aggregation behavior with monovalent and divalent salts upon the addition of humic acid to the solution. For NaCl-induced aggregation, the introduction of humic acid significantly suppressed the aggregation rate of FNPs at NaCl concentrations lower than 150mM. In this case, the aggregation was intermediate or reaction-limited even at NaCl concentrations as high as 500mM, giving rise to aggregates with a fractal dimension of 2.0. For CaCl(2)-induced aggregation, the introduction of humic acid enhanced the aggregation of FNPs at CaCl(2) concentrations greater than about 5mM due to calcium complexation and bridging effects. Humic acid also had an impact on the FNP aggregate structure in the presence of CaCl(2), resulting in a fractal dimension of 1.6 for the diffusion-limited aggregation regime. Our results with CaCl(2) indicate that in the presence of humic acid, FNP aggregates have a more open and loose structure than in the absence of humic acid. The aggregation results presented in this paper have important implications for the transport, chemical reactivity, and toxicity of engineered nanoparticles in aquatic
Local connected fractal dimension analysis in gill of fish experimentally exposed to toxicants.
Manera, Maurizio; Giari, Luisa; De Pasquale, Joseph A; Sayyaf Dezfuli, Bahram
2016-06-01
An operator-neutral method was implemented to objectively assess European seabass, Dicentrarchus labrax (Linnaeus, 1758) gill pathology after experimental exposure to cadmium (Cd) and terbuthylazine (TBA) for 24 and 48h. An algorithm-derived local connected fractal dimension (LCFD) frequency measure was used in this comparative analysis. Canonical variates (CVA) and linear discriminant analysis (LDA) were used to evaluate the discrimination power of the method among exposure classes (unexposed, Cd exposed, TBA exposed). Misclassification, sensitivity and specificity, both with original and cross-validated cases, were determined. LCFDs frequencies enhanced the differences among classes which were visually selected after their means, respective variances and the differences between Cd and TBA exposed means, with respect to unexposed mean, were analyzed by scatter plots. Selected frequencies were then scanned by means of LDA, stepwise analysis, and Mahalanobis distance to detect the most discriminative frequencies out of ten originally selected. Discrimination resulted in 91.7% of cross-validated cases correctly classified (22 out of 24 total cases), with sensitivity and specificity, respectively, of 95.5% (1 false negative with respect to 21 really positive cases) and 75% (1 false positive with respect to 3 really negative cases). CVA with convex hull polygons ensured prompt, visually intuitive discrimination among exposure classes and graphically supported the false positive case. The combined use of semithin sections, which enhanced the visual evaluation of the overall lamellar structure; of LCFD analysis, which objectively detected local variation in complexity, without the possible bias connected to human personnel; and of CVA/LDA, could be an objective, sensitive and specific approach to study fish gill lamellar pathology. Furthermore this approach enabled discrimination with sufficient confidence between exposure classes or pathological states and avoided
Comparison of different fractal dimension measuring algorithms for RE-TM M-O films
NASA Technical Reports Server (NTRS)
Bernacki, Bruce E.; Mansuripur, M.
1991-01-01
Noise in magneto-optical recording devices is discussed. In general, it appears that either the divider technique or amplitude spectrum technique may be used interchangeably to measure the fractal dimension (D) in the domain wall structure of ideal images. However, some caveats must be observed for best results. The divider technique is attractive for its simplicity and relatively modest computation requirements. However, it is sensitive to noise, in that noise pixels that touch the domain boundary are interpreted as being part of the boundary, skewing the measurement. Also, it is not useful in measuring nucleation-dominated films or domains that have significant amounts of structure within the interior of the domain wall. The amplitude spectrum method is more complex, and less intuitive than the divider method, and somewhat more expensive to implement computationally. However, since the camera noise tends to be white, the noise can be avoided in the measurement of D by avoiding that portion of the curve that is flat (due to the white noise) when the least squares line is fit to the plot. Also, many image processing software packages include a Fast Fourier Transformation (FFT) facility, while the user will most likely have to write his own edge extraction routine for the divider method. The amplitude spectrum method is a true two dimensional technique that probes the interior of the domain wall, and in fact, can measure arbitrary clusters of domains. It can also be used to measure grey-level images, further reducing processing steps needed to threshold the image.
Brain White Matter Shape Changes in Amyotrophic Lateral Sclerosis (ALS): A Fractal Dimension Study
Allexandre, Didier; Zhang, Luduan; Wang, Xiao-Feng; Pioro, Erik P.; Yue, Guang H.
2013-01-01
Amyotrophic lateral sclerosis (ALS) is a fatal progressive neurodegenerative disorder. Current diagnosis time is about 12-months due to lack of objective methods. Previous brain white matter voxel based morphometry (VBM) studies in ALS reported inconsistent results. Fractal dimension (FD) has successfully been used to quantify brain WM shape complexity in various neurological disorders and aging, but not yet studied in ALS. Therefore, we investigated WM morphometric changes using FD analyses in ALS patients with different clinical phenotypes. We hypothesized that FD would better capture clinical features of the WM morphometry in different ALS phenotypes than VBM analysis. High resolution MRI T1-weighted images were acquired in controls (n = 11), and ALS patients (n = 89). ALS patients were assigned into four subgroups based on their clinical phenotypes.VBM analysis was carried out using SPM8. FD values were estimated for brain WM skeleton, surface and general structure in both controls and ALS patients using our previously published algorithm. No significant VBM WM changes were observed between controls and ALS patients and among the ALS subgroups. In contrast, significant (p<0.05) FD reductions in skeleton and general structure were observed between ALS with dementia and other ALS subgroups. No significant differences in any of the FD measures were observed between control and ALS patients. FD correlated significantly with revised ALS functional rating scale (ALSFRS-R) score a clinical measure of function. Results suggest that brain WM shape complexity is more sensitive to ALS disease process when compared to volumetric VBM analysis and FD changes are dependent on the ALS phenotype. Correlation between FD and clinical measures suggests that FD could potentially serve as a biomarker of ALS pathophysiology, especially after confirmation by longitudinal studies. PMID:24040000
Torres, SR; Chen, CSK; Leroux, BG; Lee, PP; Hollender, LG; Schubert, MM
2011-01-01
Objectives The aim of this study was to (1) evaluate the fractal dimension (FD) in regions of the mandible on cone beam CT (CBCT) images of patients with bisphosphonate-associated osteonecrosis of the jaws (BP-ONJ) and (2) to select the most suitable region of interest (ROI) for further study on detection of bone alterations associated with bisphosphonates. Methods CBCT images of patients with BP-ONJ were included with matched controls. Values of FD were compared between groups. Selected ROIs were: ROI-1 — below the mandibular foramen; ROI-2 — above the mandibular foramen; ROI-3 — anterior to the mental foramen; ROI-4 — above the mandibular canal. The area of bone exposure was included as ROI-5. The results were analysed using generalized estimating equations and conditional logistic regression. Results There were 36 patients (67% female) with a mean age of 60.7 years. The mean FDs were: ROI-1 — 1.678 for controls and 1.673 for patients (P = 0.81); ROI-2 — 1.657 for controls and 1.653 for patients (P = 0.78); ROI-3 — 1.661 for controls and 1.684 for patients (P = 0.17); and ROI-4 — 1.670 for controls and 1.698 for patients (P = 0.03). The value of the FD in the area of exposed bone was the highest (1.729). The odds of being a BP-ONJ patient vs being a control was six times as high for individuals with a higher FD score at ROI-4, although the confidence interval was quite wide owing to the small sample size. Conclusion In this preliminary study, BP-ONJ patients had higher FD values than controls at regions close to the alveolar process. The results suggest that FD is a promising tool for detection of bone alterations associated with BP-ONJ. PMID:22065799
Simulation model of the fractal patterns in ionic conducting polymer films
NASA Astrophysics Data System (ADS)
Amir, Shahizat; Mohamed, Nor; Hashim Ali, Siti
2010-02-01
Normally polymer electrolyte membranes are prepared and studied for applications in electrochemical devices. In this work, polymer electrolyte membranes have been used as the media to culture fractals. In order to simulate the growth patterns and stages of the fractals, a model has been identified based on the Brownian motion theory. A computer coding has been developed for the model to simulate and visualize the fractal growth. This computer program has been successful in simulating the growth of the fractal and in calculating the fractal dimension of each of the simulated fractal patterns. The fractal dimensions of the simulated fractals are comparable with the values obtained in the original fractals observed in the polymer electrolyte membrane. This indicates that the model developed in the present work is within acceptable conformity with the original fractal.
NASA Astrophysics Data System (ADS)
Boness, D. A.; Terrell-Martinez, B.
2010-12-01
As part of an ongoing undergraduate research project of light scattering calculations involving fractal carbonaceous soot aggregates relevant to current anthropogenic and natural sources in Earth's atmosphere, we have read with interest a recent paper [E.T. Wolf and O.B Toon,Science 328, 1266 (2010)] claiming that the Faint Young Sun paradox discussed four decades ago by Carl Sagan and others can be resolved without invoking heavy CO2 concentrations as a greenhouse gas warming the early Earth enough to sustain liquid water and hence allow the origin of life. Wolf and Toon report that a Titan-like Archean Earth haze, with a fractal haze aggregate nature due to nitrogen-methane photochemistry at high altitudes, should block enough UV light to protect the warming greenhouse gas NH3 while allowing enough visible light to reach the surface of the Earth. To test this hypothesis, we have employed a rigorous T-Matrix arbitrary-particle light scattering technique, to avoid the simplifications inherent in Mie-sphere scattering, on haze fractal aggregates at UV and visible wavelenths of incident light. We generate these model aggregates using diffusion-limited cluster aggregation (DLCA) algorithms, which much more closely fit actual haze fractal aggregates than do diffusion-limited aggregation (DLA) algorithms.
Structural investigations of fat fractals using small-angle scattering
NASA Astrophysics Data System (ADS)
Anitas, Eugen M.
2015-01-01
Experimental small-angle scattering (SAS) data characterized, on a double logarithmic scale, by a succession of power-law decays with decreasing values of scattering exponents, can be described in terms of fractal structures with positive Lebesgue measure (fat fractals). Here we present a theoretical model for fat fractals and show how one can extract structural information about the underlying fractal using SAS method, for the well known fractals existing in the literature: Vicsek and Menger sponge. We calculate analytically the fractal structure factor and study its properties in momentum space. The models allow us to obtain the fractal dimension at each structural level inside the fractal, the number of particles inside the fractal and about the most common distances between the center of mass of the particles.
NASA Astrophysics Data System (ADS)
Flores-Marquez, E. L.; Galvez-Coyt, G.; Cifuentes-Nava, G.
2012-12-01
Fractal analysis of the total magnetic field (TMF) time series from 1997 to 2003 at Popocatépetl Volcano is performed and compared with the TMF-series of the Teoloyucan Magnetic Observatory, 100 km away. Using Higuchi's fractal dimension method (D). The D changes over time for both series were computed. It was observed, when the time windows used to compute D increase in length, both series show nearly the same behavior. Some criteria of comparison were employed to discriminate the local effects inherent to volcano-magnetism. The simultaneous maximum in D (1.8) of the TMF series at Popocatépetl Volcano and the recovered volcanic activity indicates a scaling relation of the TMF at Popocatépetl Volcano and demonstrates a link between the magnetic field and volcanic activity.
Zhang, Lihui; Duan, Feng; Huang, Yaji; Chyang, Chiensong
2015-12-01
The changes in pore structure characteristics of sewage sludge particles under effect of calcium magnesium acetate (CMA) during combustion were investigated, the samples were characterized by N2 isothermal absorption method, and the data were used to analyze the fractal properties of the obtained samples. Results show that reaction time and the mole ratio of calcium to sulfur (Ca/S ratio) have notable impact on the pore structure and morphology of solid sample. The Brunauer-Emmett-Teller (BET) specific surface area (SBET) of sample increases with Ca/S ratio, while significant decreases with reaction time. The fractal dimension D has the similar trend with that of SBET, indicating that the surface roughness of sludge increases under the effect of CMA adding, resulting in improved the sludge combustion and the desulfurization process. PMID:26342334
Crystal, Howard A.; Holman, Susan; Lui, Yvonne W.; Baird, Alison E.; Yu, Hua; Klein, Ronald; Rojas-Soto, Diana Marcella; Gustafson, Deborah R.; Stebbins, Glenn T.
2016-01-01
Objective The fractal dimension of retinal arteries and veins is a measure of the complexity of the vascular tree. We hypothesized that retinal fractal dimension would be associated with brain volume and white matter integrity in HIV-infected women. Design Nested case-control within longitudinal cohort study. Methods Women were recruited from the Brooklyn site of the Women’s Interagency HIV study (WIHS); 34 HIV-infected and 21 HIV-uninfected women with analyzable MRIs and retinal photographs were included. Fractal dimension was determined using the SIVA software program on skeletonized retinal images. The relationship between predictors (retinal vascular measures) and outcomes (quantitative MRI measures) were analyzed with linear regression models. All models included age, intracranial volume, and both arterial and venous fractal dimension. Some models were adjusted for blood pressure, race/ethnicity, and HIV-infection. Results The women were 45.6 ± 7.3 years of age. Higher arterial dimension was associated with larger cortical volumes, but higher venous dimension was associated with smaller cortical volumes. In fully adjusted models, venous dimension was significantly associated with fractional anisotropy (standardized β = -0.41, p = 0.009) and total gray matter volume (β = -0.24, p = 0.03), and arterial dimension with mean diffusivity (β = -0.33,.p = 0.04) and fractional anisotropy (β = 0.34, p = 0.03). HIV-infection was not associated with any retinal or MRI measure. Conclusions Higher venous fractal dimension was associated with smaller cortical volumes and lower fractional anisotropy, whereas higher arterial fractal dimension was associated with the opposite patterns. Longitudinal studies are needed to validate this finding. PMID:27158911
NASA Astrophysics Data System (ADS)
Suzuki, Hiroki; Nagata, Kouji; Sakai, Yasuhiko; Hasegawa, Yutaka
2013-07-01
The fractal geometry of turbulent mixing of high-Schmidt-number scalars in multiscale, fractal-generated turbulence (FGT) is experimentally investigated. The difference between the fractal geometry in FGT and that in classical grid turbulence (CGT) generated by a biplane, single-scale grid is also investigated. Nondimensional concentration fields are measured by a planar laser-induced fluorescence technique whose accuracy has recently been improved by our research group, and the fractal dimensions are calculated by using the box-counting method. The mesh Reynolds number is 2500 for both CGT and FGT. The Schmidt number is about 2100. It is found that the threshold width ΔCth, when applying the box-counting method, does not affect the evaluation of the fractal dimension at large scales; therefore, the fractal dimensions at large scales have been investigated in this study. The results show that the fractal dimension in FGT is larger than that in CGT. In addition, the fractal dimension in FGT monotonically increases with the onset of time (or with the downstream direction), whereas that in CGT is almost constant with time. The investigation of the number of counted boxes in a unit area, together with the above results, suggests that turbulent mixing is more enhanced in FGT from the viewpoints of fractal geometry and expansion of the mixing interface.
NASA Astrophysics Data System (ADS)
Albert, Helena; Perugini, Diego; Martí, Joan
2014-05-01
The volcanic unit of Montaña Reventada is an example of magma mixing in Tenerife (Canary Islands, Spain). The eruptive process has been detonated by a basanite intruding into a phonolite magma chamber. This eruption started with a basanite followed by a phonolite. Montaña Reventada phonolite is characterized by the presence of mafic enclaves. These enclaves represent about the 2% of the outcrop and have been classified like basanites, phono-tephrite and tephri-phonolite. The enclaves have different morphologies, from rounded to complex fingers-like structures, and usually exhibit cuspate terminations. This study aims to provide a new perspective on the 1100 AD Montaña Reventada eruption quantifying the textural heterogeneities related to the enclaves generated by the mixing process. The textural study was carried out using a fractal geometry approach, and its results were used to calculate some parameters related to magma chamber dynamics. Photographs of 67 samples were taken normal to the surface of the enclaves with the aim of delineating the contact between the enclaves and the host rocks. The resulted pictures were processed with the NIH (National Institutes of Health) image analysis software to generate binary images in which enclaves and host rock were replaced by black and white pixels, respectively. The fractal dimension (Dbox) has been computed by using the box-counting method in order to quantify the complexity of the enclaves morphology. Viscosity ratio (μR) between the phonolite and the enclaves has been calculated as follows: log(μR) = 0.013e3.34Dbox PIC The viscosity of the enclaves has been calculated according to the μRvalue with the higher frequency and to the calculated viscosity of the phonolite between 900° and 1200° . We hypothesized that this value corresponds to the amount of mafic magma present in the system, while the other values represent different degrees of mingling and chemical diffusion. Viscosity of the basanite can be
Building Fractal Models with Manipulatives.
ERIC Educational Resources Information Center
Coes, Loring
1993-01-01
Uses manipulative materials to build and examine geometric models that simulate the self-similarity properties of fractals. Examples are discussed in two dimensions, three dimensions, and the fractal dimension. Discusses how models can be misleading. (Contains 10 references.) (MDH)
NASA Astrophysics Data System (ADS)
Klein, D. J.; March, N. H.; Alonso, J. A.
2009-07-01
[Ma et al., Nat. Mater. 8, 30 (2009)] have uncovered the fractal dimension Df=2.31 associated with the medium-range order in a variety of bulk metallic glasses, reflected in the first sharp diffraction peak q1 determined from neutron and x-ray measurements. Here, based on the proposal in this journal of [Yang et al., Appl. Phys. Lett. 88, 221911 (2006)], which related the strength σy of bulk metallic glasses to the glass transition temperature Tg, we show that the product q1Dfσy is linear in Tg.
Lung cancer-a fractal viewpoint.
Lennon, Frances E; Cianci, Gianguido C; Cipriani, Nicole A; Hensing, Thomas A; Zhang, Hannah J; Chen, Chin-Tu; Murgu, Septimiu D; Vokes, Everett E; Vannier, Michael W; Salgia, Ravi
2015-11-01
Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed. PMID:26169924
Lung cancer—a fractal viewpoint
Lennon, Frances E.; Cianci, Gianguido C.; Cipriani, Nicole A.; Hensing, Thomas A.; Zhang, Hannah J.; Chen, Chin-Tu; Murgu, Septimiu D.; Vokes, Everett E.; W. Vannier, Michael; Salgia, Ravi
2016-01-01
Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed. PMID:26169924
NASA Astrophysics Data System (ADS)
Cámara, Joaquín; Gómez-Miguel, Vicente; Martín, Miguel Ángel
2016-03-01
Geologists know that drainage networks can exhibit different drainage patterns depending on the hydrogeological properties of the underlying materials. Geographic Information System (GIS) technologies and the increasing availability and resolution of digital elevation data have greatly facilitated the delineation, quantification, and study of drainage networks. This study investigates the possibility of inferring geological information of the underlying material from fractal and linear parameters describing drainage networks automatically extracted from 5-m-resolution LiDAR digital terrain model (DTM) data. According to the lithological information (scale 1:25,000), the study area is comprised of 30 homogeneous bedrock lithologies, the lithological map units (LMUs). These are mostly igneous and metamorphic rocks, but also include some sedimentary rocks. A statistical classification model of the LMUs by rock type has been proposed based on both the fractal dimension and drainage density of the overlying drainage networks. The classification model has been built using 16 LMUs, and it has correctly classified 13 of the 14 LMUs used for its validation. Results for the study area show that LMUs, with areas ranging from 177.83 ± 0.01 to 3.16 ± 0.01 km2, can be successfully classified by rock type using the fractal dimension and the drainage density of the drainage networks derived from medium resolution LiDAR DTM data with different flow support areas. These results imply that the information included in a 5-m-resolution LiDAR DTM and the appropriate techniques employed to manage it are the only inputs required to identify the underlying geological materials.
Sadana, A
1998-01-01
The diffusion-limited binding kinetics of antigen (analyte), in solution with antibody (receptor) immobilized on a biosensor surface, is analyzed within a fractal framework. Most of the data presented is adequately described by a single-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot. A single example of a dual-fractal analysis is also presented. It is of interest to note that the binding-rate coefficient (k) and the fractal dimension (Df) both exhibit changes in the same and in the reverse direction for the antigen-antibody systems analyzed. Binding-rate coefficient expressions, as a function of the Df developed for the antigen-antibody binding systems, indicate the high sensitivity of the k on the Df when both a single- and a dual-fractal analysis are used. For example, for a single-fractal analysis, and for the binding of antibody Mab 0.5 beta in solution to gp120 peptide immobilized on a BIAcore biosensor, the order of dependence on the Df was 4.0926. For a dual-fractal analysis, and for the binding of 25-100 ng/mL TRITC-LPS (lipopolysaccharide) in solution with polymyxin B immobilized on a fiberoptic biosensor, the order of dependence of the binding-rate coefficients, k1 and k2, on the fractal dimensions, Df1 and Df2, were 7.6335 and -11.55, respectively. The fractional order of dependence of the k(s) on the Df(s) further reinforces the fractal nature of the system. The k(s) expressions developed as a function of the Df(s) are of particular value, since they provide a means to better control biosensor performance, by linking it to the heterogeneity on the surface, and further emphasize, in a quantitative sense, the importance of the nature of the surface in biosensor performance. PMID:9779572
NASA Astrophysics Data System (ADS)
Tao, Dongwang; Mao, Chenxi; Zhang, Dongyu; Li, Hui
2014-12-01
This article extends a signal-based approach formerly proposed by the authors, which utilizes the fractal dimension of time frequency feature (FDTFF) of displacements, for earthquake damage detection of moment resist frame (MRF), and validates the approach with shaking table tests. The time frequency feature (TFF) of the relative displacement at measured story is defined as the real part of the coefficients of the analytical wavelet transform. The fractal dimension (FD) is to quantify the TFF within the fundamental frequency band using box counting method. It is verified that the FDTFFs at all stories of the linear MRF are identical with the help of static condensation method and modal superposition principle, while the FDTFFs at the stories with localized nonlinearities due to damage will be different from those at the stories without nonlinearities using the reverse-path methodology. By comparing the FDTFFs of displacements at measured stories in a structure, the damage-induced nonlinearity of the structure under strong ground motion can be detected and localized. Finally shaking table experiments on a 1:8 scale sixteen-story three-bay steel MRF with added frictional dampers, which generate local nonlinearities, are conducted to validate the approach.
NASA Astrophysics Data System (ADS)
Cymberknop, L.; Legnani, W.; Pessana, F.; Bia, D.; Zócalo, Y.; Armentano, R. L.
2011-12-01
The advent of vascular diseases, such as hypertension and atherosclerosis, is associated to significant alterations in the physical properties of arterial vessels. Evaluation of arterial biomechanical behaviour is related to the assessment of three representative indices: arterial compliance, arterial distensibility and arterial stiffness index. Elasticity is the most important mechanical property of the arterial wall, whose natures is strictly non-linear. Intervention of elastin and collagen fibres, passive constituent elements of the arterial wall, is related to the applied wall stress level. Concerning this, appropriate tools are required to analyse the temporal dynamics of the signals involved, in order to characterize the whole phenomenon. Fractal geometry can be mentioned as one of those techniques. The aim of this study consisted on arterial pressure and diameter signals processing, by means of nonlinear techniques based on fractal geometry. Time series morphology was related to different arterial stiffness states, generated by means of blood flow variations, during experiences performed in vitro.
Wagenseil, R.
1991-01-01
There are persistent difficulties in monitoring nonpoint source pollution and in the related field of hydrology. The problems stem from variations in spatial distribution which are poorly understood and difficult to model with established methods. Two recent developments may offer a solution, if they are combined with care. The first development is the increasing capability of computer mapping, called geographic information systems (GIS). These systems can store, retrieve, and manipulate data with an explicit spatial structure. The second development is the field of fractal mathematics. Fractal mathematics includes geometric sets which have simple descriptions, despite complex appearances. One family of such fractal sets are the Brownian surfaces, which capture many of the qualities of natural land surfaces in a simple statistical model. Up until now, the Brownian models have been constrained by the assumption that the same statistical relationship holds over the entire surface. This is called the constraint of stationarity. The need to study how the landscape differs by location leads to relaxing the constraint of stationarity. This, in turn, causes some profound changes in the model. A special computer program applies the new model to a set of three-dimensional digital maps of natural terrain (DEMs). The model performs well, and highlights differences in landforms. This suggests several new approaches to spatial variation.
Comprehensive Fractal Description of Porosity of Coal of Different Ranks
Ren, Jiangang; Zhang, Guocheng; Song, Zhimin; Liu, Gaofeng; Li, Bing
2014-01-01
We selected, as the objects of our research, lignite from the Beizao Mine, gas coal from the Caiyuan Mine, coking coal from the Xiqu Mine, and anthracite from the Guhanshan Mine. We used the mercury intrusion method and the low-temperature liquid nitrogen adsorption method to analyze the structure and shape of the coal pores and calculated the fractal dimensions of different aperture segments in the coal. The experimental results show that the fractal dimension of the aperture segment of lignite, gas coal, and coking coal with an aperture of greater than or equal to 10 nm, as well as the fractal dimension of the aperture segment of anthracite with an aperture of greater than or equal to 100 nm, can be calculated using the mercury intrusion method; the fractal dimension of the coal pore, with an aperture range between 2.03 nm and 361.14 nm, can be calculated using the liquid nitrogen adsorption method, of which the fractal dimensions bounded by apertures of 10 nm and 100 nm are different. Based on these findings, we defined and calculated the comprehensive fractal dimensions of the coal pores and achieved the unity of fractal dimensions for full apertures of coal pores, thereby facilitating, overall characterization for the heterogeneity of the coal pore structure. PMID:24955407
NASA Astrophysics Data System (ADS)
Davarpanah, Armita; Babaie, Hassan A.
2013-11-01
The Basin and Range fault blocks, which were formed by an extensional event around 17 Ma, have continuously been deforming by younger, diachronous system of cross normal faults in southwest Montana and southeastern Idaho since 16.6 Ma. Reactivation of these two mid-Tertiary-Quaternary systems of normal faults, and two older, approximately N-S and E-W sets of regional normal faults, has evolved into a seismically active block faulted terrain. For both fault systems, high fractal dimensions occur in areas characterized by a large number of fault traces, high fault trace linear density, and maximum fault trace azimuthal variation. The major axis of the anisotropy ellipse of the fractal dimensions for each set of the two normal fault systems is sub-perpendicular to the linear directional mean of the faults, and gives an estimate for the direction of extension. Indentations on the point distribution on the anisotropy ellipse of fractal dimensions indicate heterogeneities due to the presence of several fault sets and/or variation in their trend. Domains in which there is only one set of faults produce smooth, well-defined fractal anisotropy ellipses with no indentations. The axial ratio of the anisotropy ellipse provides a measure for the range of variation in the trend of the faults. The trace length, linear density, and fractal dimension of the cross normal faults, decrease, in a direction across and away from the Snake River Plain (SRP), suggesting a diminishing effect of faulting probably due to the attenuation of the Yellowstone hotspot-related thermal doming with distance from centers of eruption. The spatio-temporal distribution of the trajectories of the minor axes of the anisotropy ellipses of fractal dimensions and the linear directional mean of the cross faults define a set of asymmetric, sub-parabolic spatio-temporal pattern about the axis of the SRP, with their apices located on diachronous centers of eruption.
Sorensen, C M; Cai, J; Lu, N
1992-10-20
A new method for the in situ optical determination of the soot-cluster monomer particle radius a, the number of monomers per cluster N, and the fractal dimension D is presented. The method makes use of a comparison of the volume-equivalent sphere radius determined from scattering-extinction measurements RSe and the radius of gyration Rg, which is determined from the optical structure factor. The combination of these data with the measured turbidity permits for a novel measurement of D. The parameters a and N are obtained from a graphical network-analysis scheme that compares R(se) and Rg. Corrections for cluster polydispersity are presented. The effects of uncertainty in various input parameters and assumptions are discussed. The method is illustrated by an application to data obtained from a premixed methane-oxygen flame, and reasonable values of a, N, andD are obtained. PMID:20733873
Berry, Hugues
2002-01-01
Conventional equations for enzyme kinetics are based on mass-action laws, that may fail in low-dimensional and disordered media such as biological membranes. We present Monte Carlo simulations of an isolated Michaelis-Menten enzyme reaction on two-dimensional lattices with varying obstacle densities, as models of biological membranes. The model predicts that, as a result of anomalous diffusion on these low-dimensional media, the kinetics are of the fractal type. Consequently, the conventional equations for enzyme kinetics fail to describe the reaction. In particular, we show that the quasi-stationary-state assumption can hardly be retained in these conditions. Moreover, the fractal characteristics of the kinetics are increasingly pronounced as obstacle density and initial substrate concentration increase. The simulations indicate that these two influences are mainly additive. Finally, the simulations show pronounced S-P segregation over the lattice at obstacle densities compatible with in vivo conditions. This phenomenon could be a source of spatial self organization in biological membranes. PMID:12324410
Cake porosity analysis using 1D-3D fractal dimensions in coagulation-microfiltration of NOM.
Raspati, G S; Leiknes, T O
2015-01-01
Fouling during coagulation-ceramic microfiltration of natural organic matter was investigated. Two process configurations (inline coagulation (IC) and tank coagulation (TC)) and two process conditions (types of coagulants-aluminum-based PAX and iron-based PIX-and G-values) were studied. The rate of irreversible fouling corresponding to the increase of initial transmembrane pressure after backwash of IC-PAX was lowest followed by TC-PAX and TC-PIX, while the performance of IC-PIX was found worst. The 1D and 2D fractal analysis revealed that flocs from IC were morphologically different from those of TC, leading to different filtration characteristics. The 3D fractal analysis revealed two groups of morphologically similar flocs: one led to successful filtration experiments, whereas the other led to unsuccessful ones. Cake porosity was found dependent on the floc morphology. Thus, such an approach was found complementary with fouling analysis by means of a membrane fouling model and minimization of fouling phenomenon was achieved by combining the two approaches. PMID:25768221
Verifying the Dependence of Fractal Coefficients on Different Spatial Distributions
Gospodinov, Dragomir; Marekova, Elisaveta; Marinov, Alexander
2010-01-21
A fractal distribution requires that the number of objects larger than a specific size r has a power-law dependence on the size N(r) = C/r{sup D}propor tor{sup -D} where D is the fractal dimension. Usually the correlation integral is calculated to estimate the correlation fractal dimension of epicentres. A 'box-counting' procedure could also be applied giving the 'capacity' fractal dimension. The fractal dimension can be an integer and then it is equivalent to a Euclidean dimension (it is zero of a point, one of a segment, of a square is two and of a cube is three). In general the fractal dimension is not an integer but a fractional dimension and there comes the origin of the term 'fractal'. The use of a power-law to statistically describe a set of events or phenomena reveals the lack of a characteristic length scale, that is fractal objects are scale invariant. Scaling invariance and chaotic behavior constitute the base of a lot of natural hazards phenomena. Many studies of earthquakes reveal that their occurrence exhibits scale-invariant properties, so the fractal dimension can characterize them. It has first been confirmed that both aftershock rate decay in time and earthquake size distribution follow a power law. Recently many other earthquake distributions have been found to be scale-invariant. The spatial distribution of both regional seismicity and aftershocks show some fractal features. Earthquake spatial distributions are considered fractal, but indirectly. There are two possible models, which result in fractal earthquake distributions. The first model considers that a fractal distribution of faults leads to a fractal distribution of earthquakes, because each earthquake is characteristic of the fault on which it occurs. The second assumes that each fault has a fractal distribution of earthquakes. Observations strongly favour the first hypothesis.The fractal coefficients analysis provides some important advantages in examining earthquake spatial
Fractal characteristics of fracture morphology of steels irradiated with high-energy ions
NASA Astrophysics Data System (ADS)
Xian, Yongqiang; Liu, Juan; Zhang, Chonghong; Chen, Jiachao; Yang, Yitao; Zhang, Liqing; Song, Yin
2015-06-01
A fractal analysis of fracture surfaces of steels (a ferritic/martensitic steel and an oxide-dispersion-strengthened ferritic steel) before and after the irradiation with high-energy ions is presented. Fracture surfaces were acquired from a tensile test and a small-ball punch test (SP). Digital images of the fracture surfaces obtained from scanning electron microscopy (SEM) were used to calculate the fractal dimension (FD) by using the pixel covering method. Boundary of binary image and fractal dimension were determined with a MATLAB program. The results indicate that fractal dimension can be an effective parameter to describe the characteristics of fracture surfaces before and after irradiation. The rougher the fracture surface, the larger the fractal dimension. Correlation of the change of fractal dimension with the embrittlement of the irradiated steels is discussed.
A fractal analysis of quaternary, Cenozoic-Mesozoic, and Late Pennsylvanian sea level changes
NASA Technical Reports Server (NTRS)
Hsui, Albert T.; Rust, Kelly A.; Klein, George D.
1993-01-01
Sea level changes are related to both climatic variations and tectonic movements. The fractal dimensions of several sea level curves were compared to a modern climatic fractal dimension of 1.26 established for annual precipitation records. A similar fractal dimension (1.22) based on delta(O-18/O-16) in deep-sea sediments has been suggested to characterize climatic change during the past 2 m.y. Our analysis indicates that sea level changes over the past 150,000 to 250,000 years also exhibit comparable fractal dimensions. Sea level changes for periods longer than about 30 m.y. are found to produce fractal dimensions closer to unity and Missourian (Late Pennsylvanian) sea level changes yield a fractal dimension of 1.41. The fact that these sea level curves all possess fractal dimensions less than 1.5 indicates that sea level changes exhibit nonperiodic, long-run persistence. The different fractal dimensions calculated for the various time periods could be the result of a characteristic overprinting of the sediment recored by prevailing processes during deposition. For example, during the Quaternary, glacio-eustatic sea level changes correlate well with the present climatic signature. During the Missourian, however, mechanisms such as plate reorganization may have dominated, resulting in a significantly different fractal dimension.
Local Box-Counting to Determine Fractal Dimension of High-Order Chaos
NASA Astrophysics Data System (ADS)
Osaka, Motohisa; Ito, Nobuyasu
To determine the attractor dimension of chaotic dynamics, the box-counting method has the difficulty in getting accurate estimates because the boxes are not weighted by their relative probabilities. We present a new method to minimize this difficulty. The local box-counting method can be quite effective in determining the attractor dimension of high-order chaos as well as low-order chaos.
Beretta-Piccoli, Matteo; D’Antona, Giuseppe; Barbero, Marco; Fisher, Beth; Dieli-Conwright, Christina M.; Clijsen, Ron; Cescon, Corrado
2015-01-01
Purpose Over the past decade, linear and non-linear surface electromyography descriptors for central and peripheral components of fatigue have been developed. In the current study, we tested fractal dimension (FD) and conduction velocity (CV) as myoelectric descriptors of central and peripheral fatigue, respectively. To this aim, we analyzed FD and CV slopes during sustained fatiguing contractions of the quadriceps femoris in healthy humans. Methods A total of 29 recreationally active women (mean age±standard deviation: 24±4 years) and two female elite athletes (one power athlete, age 24 and one endurance athlete, age 30 years) performed two knee extensions: (1) at 20% maximal voluntary contraction (MVC) for 30 s, and (2) at 60% MVC held until exhaustion. Surface EMG signals were detected from the vastus lateralis and vastus medialis using bidimensional arrays. Results Central and peripheral fatigue were described as decreases in FD and CV, respectively. A positive correlation between FD and CV (R=0.51, p<0.01) was found during the sustained 60% MVC, probably as a result of simultaneous motor unit synchronization and a decrease in muscle fiber CV during the fatiguing task. Conclusions Central and peripheral fatigue can be described as changes in FD and CV, at least in young, healthy women. The significant correlation between FD and CV observed at 60% MVC suggests that a mutual interaction between central and peripheral fatigue can arise during submaximal isometric contractions. PMID:25880369
NASA Astrophysics Data System (ADS)
Foresti, M. L.; Valle, G.; Bonetto, R.; Ferreira, M. L.; Briand, L. E.
2010-01-01
Lipase B from Candida Antarctica (also known as Candida antarctica lipase B or CALB) was immobilized onto titanium dioxide (TiO 2) in a buffer-free, bidistilled aqueous medium. The adsorption isotherm was determined by UV-vis analysis of supernatant solution at 280 nm, revealing that in 7 h 98% of the theoretical lipase monolayer on the TiO 2 (with 45.7 m 2/g BET area) was achieved. Samples withdrawn from the supernatant immobilization medium were analyzed by Fourier-transform infrared spectroscopy in the 1700-1600 cm -1 range (where the Amide I Proteins band appears) in order to obtain quantitative information on the evolution of the secondary-structure elements of the protein. The analysis performed revealed that lipase conformation suffers only minor changes during its adsorption onto TiO 2. However, water associated to the lipase may interact of several ways with the surface of the hydrated oxide. Characterization of the immobilized biocatalyst (CALB/TiO 2) implied SEM, fractal dimension analysis and FTIR techniques. A proposal of lipase-hydrated oxide interaction is presented.
de Oliveira, Marcos Aurélio Barboza; Brandi, Antônio Carlos; dos Santos, Carlos Alberto; Botelho, Paulo Henrique Husseni; Cortez, José Luís Lasso; de Godoy, Moacir Fernandes; Braile, Domingo Marcolino
2014-01-01
Introduction Solutions that cause elective cardiac arrest are constantly evolving, but the ideal compound has not yet been found. The authors compare a new cardioplegic solution with histidine-tryptophan-glutamate (Group 2) and other one with histidine-tryptophan-cetoglutarate (Group 1) in a model of isolated rat heart. Objective To quantify the fractal dimension and Shannon entropy in rat myocytes subjected to cardioplegia solution using histidine-tryptophan with glutamate in an experimental model, considering the caspase markers, IL-8 and KI-67. Methods Twenty male Wistar rats were anesthetized and heparinized. The chest was opened, the heart was withdrawn and 40 ml/kg of cardioplegia (with histidine-tryptophan-cetoglutarate or histidine-tryptophan-glutamate solution) was infused. The hearts were kept for 2 hours at 4ºC in the same solution, and thereafter placed in the Langendorff apparatus for 30 min with Ringer-Locke solution. Analyzes were performed for immunohistochemical caspase, IL-8 and KI-67. Results The fractal dimension and Shannon entropy were not different between groups histidine-tryptophan-glutamate and histidine-tryptophan-acetoglutarate. Conclusion The amount of information measured by Shannon entropy and the distribution thereof (given by fractal dimension) of the slices treated with histidine-tryptophan-cetoglutarate and histidine-tryptophan-glutamate were not different, showing that the histidine-tryptophan-glutamate solution is as good as histidine-tryptophan-acetoglutarate to preserve myocytes in isolated rat heart. PMID:25140464
2014-01-01
Background The evaluation of intestinal trophism, mainly the mucosal layer, is an important issue in various conditions associated with injury, atrophy, recovery, and healing of the gut. The aim of the present study was to evaluate the kinetics of the proliferation and apoptosis of enterocytes by immunohistochemistry and to assess the complexity of intestinal mucosa by fractal dimension (FD) analysis in Solea solea fed different experimental diets. Results Histomorphological evaluation of all intestinal segments did not show signs of degeneration or inflammation. Cell proliferation index and FD were significantly reduced with a diet high in mussel meal (MM; p = 0.0034 and p = 0.01063, respectively), while apoptotic index did not show any significant difference for the same comparison (p = 0.3859). Linear regression analysis between apoptotic index (independent variable) and FD (dependent variable) showed a statistically significant inverse relationship (p = 0.002528). Linear regression analysis between cell proliferation index (independent variable) and FD (dependent variable) did not show any significant correlation (p = 0.131582). Conclusions The results demonstrated that diets containing increasing levels of mussel meal in substitution of fishmeal did not incite a hyperplastic response of the intestinal mucosa. The mussel meal, which is derived from molluscs, could mimic the characteristics of the sole’s natural prey, being readily digestible, even without increasing the absorptive surface of intestinal mucosa. Interestingly, from this study emerged that FD could be used as a numeric indicator complementary to in situ quantification methods to measure intestinal trophism, in conjunction with functional parameters. PMID:24997003
Ali, Zulfiqar; Elamvazuthi, Irraivan; Alsulaiman, Mansour; Muhammad, Ghulam
2016-01-01
Voice disorders are associated with irregular vibrations of vocal folds. Based on the source filter theory of speech production, these irregular vibrations can be detected in a non-invasive way by analyzing the speech signal. In this paper we present a multiband approach for the detection of voice disorders given that the voice source generally interacts with the vocal tract in a non-linear way. In normal phonation, and assuming sustained phonation of a vowel, the lower frequencies of speech are heavily source dependent due to the low frequency glottal formant, while the higher frequencies are less dependent on the source signal. During abnormal phonation, this is still a valid, but turbulent noise of source, because of the irregular vibration, affects also higher frequencies. Motivated by such a model, we suggest a multiband approach based on a three-level discrete wavelet transformation (DWT) and in each band the fractal dimension (FD) of the estimated power spectrum is estimated. The experiments suggest that frequency band 1-1562 Hz, lower frequencies after level 3, exhibits a significant difference in the spectrum of a normal and pathological subject. With this band, a detection rate of 91.28 % is obtained with one feature, and the obtained result is higher than all other frequency bands. Moreover, an accuracy of 92.45 % and an area under receiver operating characteristic curve (AUC) of 95.06 % is acquired when the FD of all levels is fused. Likewise, when the FD of all levels is combined with 22 Multi-Dimensional Voice Program (MDVP) parameters, an improvement of 2.26 % in accuracy and 1.45 % in AUC is observed. PMID:26531753
MAGNUS-3D: Accelerator magnet calculations in 3-dimensions
NASA Astrophysics Data System (ADS)
Pissanetzky, S.
1988-12-01
MAGNUS-3D is a professional finite element code for nonlinear magnetic engineering. MAGNUS-3D can solve numerically any general problem of linear or nonlinear magnetostatics in three dimensions. The problem is formulated in a domain with Dirichlet, Neumann or periodic boundary conditions, that can contain any combination of conductors of any shape in space, nonlinear magnetic materials with magnetic properties specified by magnetization tables, and nonlinear permanent magnets with any given demagnetization curve. MAGNUS-3D uses the two-scalar-potentials formulation of Magnetostatics and the finite element method, has an automatic 3D mesh generator, and advanced post-processing features that include graphics on a variety of supported devices, tabulation, and calculation of design quantities required in Magnetic Engineering. MAGNUS-3D is a general purpose 3D code, but it has been extensively used for accelerator work and many special features required for accelerator engineering have been incorporated into the code. One of such features is the calculation of field harmonic coefficients averaged in the direction of the beam, so important for the design of magnet ends. Another feature is its ability to calculate line integrals of any field component along the direction of the beam, or plot the field as a function of the z coordinate. MAGNUS-3D has found applications to the design of accelerator magnets and spectrometers, steering magnets, wigglers and undulators for free electron lasers, microtrons and magnets for synchrotron light sources, as well as magnets for NMR and medical applications, recording heads and various magnetic devices. There are three more programs closely associated with MAGNUS-3D. MAGNUS-GKS is the graphical postprocessor for the package; it supports a numer of output devices, including color vector or bit map devices. WIRE is an independent program that can calculate the field produced by any configuration of electric conductors in space, at any
NASA Astrophysics Data System (ADS)
Aklouche Benouaguef, S.; Zeghmati, B.; Bouhadef, K.; Daguenet, M.
In this study, we investigated numerically the transient natural convection in a square cavity with two horizontal adiabatic sides and vertical walls composed of two regions of same size maintained at different temperatures. The flow has been assumed to be laminar and bi-dimensional. The governing equations written in dimensionless form and expressed in terms of stream function and vorticity, have been solved using the Alternating Direction Implicit (ADI) method and the GAUSS elimination method. Calculations were performed for air (Pr = 0.71), with a Rayleigh number varying from 2.5x105 to 3.7x106. We analysed the effect of the Rayleigh number on the route to the chaos of the system. The first transition has been found from steady-state to oscillatory flow and the second is a subharmonic bifurcation as the Rayleigh number is increased further. For sufficiently small Rayleigh numbers, present results show that the flow is characterized by four cells with horizontal and vertical symmetric axes. The attractor bifurcates from a stable fixed point to a limit cycle for a Rayleigh number varying from 2.5x105 to 2.51x105. A limit cycle settles from Ra = 3x105 and persists until Ra = 5x105. At a Rayleigh number of 2.5x105 the temporal evolution of the Nusselt number Nu(t) was stationary. As the Rayleigh number increases, the flow becomes unstable and bifurcates to a time periodic solution at a critical Rayleigh number between 2.5x105 and 2.51x105. After the first HOPF bifurcation at Ra = 2.51x105, the oscillatory flow undergoes several bifurcations and ultimately evolves into a chaotic flow.
NASA Technical Reports Server (NTRS)
Wiscombe, W.
1999-01-01
The purpose of this paper is discuss the concept of fractal dimension; multifractal statistics as an extension of this; the use of simple multifractal statistics (power spectrum, structure function) to characterize cloud liquid water data; and to understand the use of multifractal cloud liquid water models based on real data as input to Monte Carlo radiation models of shortwave radiation transfer in 3D clouds, and the consequences of this in two areas: the design of aircraft field programs to measure cloud absorptance; and the explanation of the famous "Landsat scale break" in measured radiance.
NASA Astrophysics Data System (ADS)
Davarpanah, A.; Babaie, H. A.
2012-12-01
The interaction of the thermally induced stress field of the Yellowstone hotspot (YHS) with existing Basin and Range (BR) fault blocks, over the past 17 m.y., has produced a new, spatially and temporally variable system of normal faults around the Snake River Plain (SRP) in Idaho and Wyoming-Montana area. Data about the trace of these new cross faults (CF) and older BR normal faults were acquired from a combination of satellite imageries, DEM, and USGS geological maps and databases at scales of 1:24,000, 1:100,000, 1:250,000, 1:1000, 000, and 1:2,500, 000, and classified based on their azimuth in ArcGIS 10. The box-counting fractal dimension (Db) of the BR fault traces, determined applying the Benoit software, and the anisotropy intensity (ellipticity) of the fractal dimensions, measured with the modified Cantor dust method applying the AMOCADO software, were measured in two large spatial domains (I and II). The Db and anisotropy of the cross faults were studied in five temporal domains (T1-T5) classified based on the geologic age of successive eruptive centers (12 Ma to recent) of the YHS along the eastern SRP. The fractal anisotropy of the CF system in each temporal domain was also spatially determined in the southern part (domain S1), central part (domain S2), and northern part (domain S3) of the SRP. Line (fault trace) density maps for the BR and CF polylines reveal a higher linear density (trace length per unit area) for the BR traces in the spatial domain I, and a higher linear density of the CF traces around the present Yellowstone National Park (S1T5) where most of the seismically active faults are located. Our spatio-temporal analysis reveals that the fractal dimension of the BR system in domain I (Db=1.423) is greater than that in domain II (Db=1.307). It also shows that the anisotropy of the fractal dimension in domain I is less eccentric (axial ratio: 1.242) than that in domain II (1.355), probably reflecting the greater variation in the trend of the BR
Targets detection in smoke-screen image sequences using fractal and rough set theory
NASA Astrophysics Data System (ADS)
Yan, Xiaoke
2015-08-01
In this paper, a new algorithm for the detection of moving targets in smoke-screen image sequences is presented, which can combine three properties of pixel: grey, fractal dimensions and correlation between pixels by Rough Set. The first step is to locate and extract regions that may contain objects in an image by locally grey threshold technique. Secondly, the fractal dimensions of pixels are calculated, Smoke-Screen is done at different fractal dimensions. Finally, according to temporal and spatial correlations between different frames, the singular points can be filtered. The experimental results show that the algorithm can effectively increase detection probability and has robustness.
Waliszewski, Przemyslaw
2016-01-01
Background: Tumor grading, PSA concentration, and stage determine a risk of prostate cancer patients with accuracy of about 70%. An approach based on the fractal geometrical model was proposed to eliminate subjectivity from the evaluation of tumor aggressiveness and to improve the prediction. This study was undertaken to validate classes of equivalence for the spatial distribution of cancer cell nuclei in a larger, independent set of prostate carcinomas. Methods: The global fractal capacity D0, information D1 and correlation D2 dimension, the local fractal dimension (LFD) and the local connected fractal dimension (LCFD), Shannon entropy H and lacunarity λ were measured using computer algorithms in digitalized images of both the reference set (n = 60) and the test set (n = 208) of prostate carcinomas. Results: Prostate carcinomas were re-stratified into seven classes of equivalence. The cut-off D0-values 1.5450, 1.5820, 1.6270, 1.6490, 1.6980, 1.7640 defined the classes from C1 to C7, respectively. The other measures but the D1 failed to define the same classes of equivalence. The pairs (D0, LFD), (D0, H), (D0, λ), (D1, LFD), (D1, H), (D1, λ) characterized the spatial distribution of cancer cell nuclei in each class. The co-application of those measures enabled the subordination of prostate carcinomas to one out of three clusters associated with different tumor aggressiveness. For D0 < 1.5820, LFD < 1.3, LCFD > 1.5, H < 0.7, and λ > 0.8, the class C1 or C2 contains low complexity low aggressive carcinomas exclusively. For D0 > 1.6980, LFD > 1.7644, LCFD > 1.7051, H > 0.9, and λ < 0.7, the class C6 or C7 contains high complexity high aggressive carcinomas. Conclusions: The cut-off D0-values defining the classes of equivalence were validated in this study. The cluster analysis suggested that the number of the subjective Gleason grades and the number of the objective classes of equivalence could be decreased from seven to three without a loss of clinically
Fractal characteristics of ozonometric network
NASA Technical Reports Server (NTRS)
Gruzdev, Alexander N.
1994-01-01
The fractal (correlation) dimensions are calculated which characterize the distribution of stations in the ground-based total ozone measuring network and the distribution of nodes in a latitude-longitude grid. The dimension of the ground-based ozonometric network equals 1.67 +/- 0.1 with an appropriate scaling in the 60 to 400 km range. For the latitude-longitude grid two scaling regimes are revealed. One regime, with the dimension somewhat greater than one, is peculiar to smaller scales and limited from a larger scale by the latitudinal resolution of the grid. Another scaling regime, with the dimension equal 1.84, ranges up to 15,000 km scale. The fact that the dimension of a measuring network is less than two possesses problems in observing sparse phenomena. This has to have important consequences for ozone statistics.
Persistence intervals of fractals
NASA Astrophysics Data System (ADS)
Máté, Gabriell; Heermann, Dieter W.
2014-07-01
Objects and structures presenting fractal like behavior are abundant in the world surrounding us. Fractal theory provides a great deal of tools for the analysis of the scaling properties of these objects. We would like to contribute to the field by analyzing and applying a particular case of the theory behind the P.H. dimension, a concept introduced by MacPherson and Schweinhart, to seek an intuitive explanation for the relation of this dimension and the fractality of certain objects. The approach is based on recently elaborated computational topology methods and it proves to be very useful for investigating scaling hidden in dimensions lower than the “native” dimension in which the investigated object is embedded. We demonstrate the applicability of the method with two examples: the Sierpinski gasket-a traditional fractal-and a two dimensional object composed of short segments arranged according to a circular structure.
Dimension of chaotic attractors
Farmer, J.D.; Ott, E.; Yorke, J.A.
1982-09-01
Dimension is perhaps the most basic property of an attractor. In this paper we discuss a variety of different definitions of dimension, compute their values for a typical example, and review previous work on the dimension of chaotic attractors. The relevant definitions of dimension are of two general types, those that depend only on metric properties, and those that depend on probabilistic properties (that is, they depend on the frequency with which a typical trajectory visits different regions of the attractor). Both our example and the previous work that we review support the conclusion that all of the probabilistic dimensions take on the same value, which we call the dimension of the natural measure, and all of the metric dimensions take on a common value, which we call the fractal dimension. Furthermore, the dimension of the natural measure is typically equal to the Lyapunov dimension, which is defined in terms of Lyapunov numbers, and thus is usually far easier to calculate than any other definition. Because it is computable and more physically relevant, we feel that the dimension of the natural measure is more important than the fractal dimension.
NASA Astrophysics Data System (ADS)
Yang, Yang; Wang, Ya Ping; Li, Chunyan; Gao, Shu; Shi, Benwei; Zhou, Liang; Wang, Dandan; Li, Gaocong; Dai, Chen
2016-04-01
Interactions between turbulence, suspended sediment concentration (SSC), settling velocity, effective density, fractal dimension, and floc size were studied on the tide-dominated, muddy coastal shelf of the southwestern Yellow Sea, China. The measurements were carried out in July 2013 at two sites located in water depths of 21.2 and 22.1 m. Negative correlations were observed between shear rate, SSC, effective density, and mean floc size, which supports the results of previous numerical, experimental, and field studies. A significant positive correlation was observed between near-bed SSC and shear rate, an indication that SSC variations are controlled by turbulence and re-suspension. In addition, significant linear relationships were found between settling velocity and other parameters (floc size, turbulence, SSC, effective density, and fractal dimension) at the two sites, indicating that the controlling factors on settling velocity are spatially variable. Principal component analysis was applied to determine the relative importance of turbulence, flocculation ability, and SSC as controls on floc size in situ. The relative contributions of turbulence, flocculation ability, and SSC to floc size (at both sites) were ~33.0%, 30.3%, and 29.7%, respectively, this being a new field-based quantitative analysis of the controls on floc size. The findings demonstrate that, in nature, flocculation ability affects floc size to the same degree as turbulence and SSC. Therefore, predictions of floc size in coastal marine environments require constraints not only on turbulence and SSC, but also on flocculation ability.
Fractal Analysis of Gas Diffusion in Porous Nanofibers
NASA Astrophysics Data System (ADS)
Xiao, Boqi; Fan, Jintu; Wang, Zongchi; Cai, Xin; Zhao, Xige
2015-02-01
In this study, with the consideration of pore size distribution and tortuosity of capillaries, the analytical model for gas diffusivity of porous nanofibers is derived based on fractal theory. The proposed fractal model for the normalized gas diffusivity (De/D0) is found to be a function of the porosity, the area fractal dimensions of pore and the fractal dimension of tortuous capillaries. It is found that the normalized gas diffusivity decreases with increasing of the tortuosity fractal dimension. However, the normalized gas diffusivity is positively correlated with the porosity. The prediction of the proposed fractal model for porous nanofibers with porosity less than 0.75 is highly consistent with the experimental and analytical results found in the literature. The model predictions are compared with the previously reported experimental data, and are in good agreement between the model predictions and experimental data is found. The validity of the present model is thus verified. Every parameter of the proposed formula of calculating the normalized gas diffusivity has clear physical meaning. The proposed fractal model can reveal the physical mechanisms of gas diffusion in porous nanofibers.
Gravitation theory in a fractal space-time
Agop, M.; Gottlieb, I.
2006-05-15
Assimilating the physical space-time with a fractal, a general theory is built. For a fractal dimension D=2, the virtual geodesics of this space-time implies a generalized Schroedinger type equation. Subsequently, a geometric formulation of the gravitation theory on a fractal space-time is given. Then, a connection is introduced on a tangent bundle, the connection coefficients, the Riemann curvature tensor and the Einstein field equation are calculated. It results, by means of a dilation operator, the equivalence of this model with quantum Einstein gravity.
Mossotti, Victor G.; Eldeeb, A. Raouf; Oscarson, Robert
1998-01-01
MORPH-I is a set of C-language computer programs for the IBM PC and compatible minicomputers. The programs in MORPH-I are used for the fractal analysis of scanning electron microscope and electron microprobe images of pore profiles exposed in cross-section. The program isolates and traces the cross-sectional profiles of exposed pores and computes the Richardson fractal dimension for each pore. Other programs in the set provide for image calibration, display, and statistical analysis of the computed dimensions for highly complex porous materials. Requirements: IBM PC or compatible; minimum 640 K RAM; mathcoprocessor; SVGA graphics board providing mode 103 display.
Map of fluid flow in fractal porous medium into fractal continuum flow.
Balankin, Alexander S; Elizarraraz, Benjamin Espinoza
2012-05-01
This paper is devoted to fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow d(s) is equal to its mass fractal dimension D, even when the spectral dimension of the fractally porous or fissured medium is less than D. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided. PMID:23004869
Map of fluid flow in fractal porous medium into fractal continuum flow
NASA Astrophysics Data System (ADS)
Balankin, Alexander S.; Elizarraraz, Benjamin Espinoza
2012-05-01
This paper is devoted to fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow ds is equal to its mass fractal dimension D, even when the spectral dimension of the fractally porous or fissured medium is less than D. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided.
Cluster-Cluster Aggregation Calculations of Fractal Haze Particles: Titan and the Early Earth
NASA Astrophysics Data System (ADS)
Terrell-Martinez, Bernice; Boness, David
2010-10-01
The atmosphere of the Archean Earth (3.8 to 2.5 billion years ago) is thought to have been dominated by a thick hydrocarbon haze similar to that of Titan's current atmosphere. To understand radiative transport in the atmospheres of the early Earth and of Titan, it is necessary to compute light scattering in UV, visible, and IR wavelength ranges for realistic fractal aggregate hydrocarbon aerosol particles. We report preliminary work on MATLAB, True BASIC, and Fortran programs to simulate the growth of fractal aggregate aerosols through diffusion limited aggregation (DLA) and cluster-cluster aggregation (CCA) physical processes. The results of these computations are being used with a T-Matrix light scattering program to test recently published, widely-reported conclusions about the early Earth and the faint young Sun paradox [E. T. Wolf and O. B. Toon, Science 328, 1266 (2010)]. This modeling is also relevant to understanding atmospheric carbonaceous soot aerosol anthropogenic and natural effects on climate change of Earth today.
Fractal characterization of fracture surfaces in concrete
Saouma, V.E.; Barton, C.C.; Gamaleldin, N.A.
1990-01-01
Fractal geometry is used to characterize the roughness of cracked concrete surfaces through a specially built profilometer, and the fractal dimension is subsequently correlated to the fracture toughness and direction of crack propagation. Preliminary results indicate that the fracture surface is indeed fractal over two orders of magnitudes with a dimension of approximately 1.20. ?? 1990.
Fractal analysis of time varying data
Vo-Dinh, Tuan; Sadana, Ajit
2002-01-01
Characteristics of time varying data, such as an electrical signal, are analyzed by converting the data from a temporal domain into a spatial domain pattern. Fractal analysis is performed on the spatial domain pattern, thereby producing a fractal dimension D.sub.F. The fractal dimension indicates the regularity of the time varying data.
Shono, H; Shono, M; Iwasaka, T; Sugimori, H
2001-01-01
Human fetal heart rate (HR) variabilities were analyzed using the QIS-A, which we devised to determine a fractal dimension of non-stationary time series. Fifteen 10-min HR data of an anencephalic fetus at 23 weeks and 3 days of gestation and those of 10 normal fetuses at the same weeks of gestation were obtained by ultrasonic cardiography. The anencephalus preserved the spinal cord, medulla and partial anterior hypothalamus. The fractal scaling exponent alpha of the anencephalus was compared with that of each normal fetus by Student's t-test. In results, the scaling relationship in each case had a crossover pattern characterized by alpha(s) and alpha(l), which were slopes above and below a crossover point, respectively. Differences in mean alpha(s) and mean alpha(l) between the anencephalus and each normal fetus were significant (P < 0.01): mean alpha(s), 1.0 +/- 0.1 (+/-SD) (1/f fluctuation) and 1.6 +/- 0.2 (+/-SEM); mean alpha(l), 1.6 +/- 0.2 (+/-SD) and 1.4 +/- 0.1 (+/-SEM). There were six significant differences in mean crossover point between the anencephalus and each normal fetus: 13.8 +/- 5.7 s (+/-SD) and 15.3 +/- 5.6 s (+/-SEM). These results reveal the relationship between fractal structure of fetal HR variability and the developing central nervous system (CNS). In particular, the 1/f fluctuation of HR variability in an anencephalic fetus from the 1.25 to 13.8 s time scale might have a strong relation to the defect of the CNS. PMID:11334172
Fractal Geometry of Architecture
NASA Astrophysics Data System (ADS)
Lorenz, Wolfgang E.
In Fractals smaller parts and the whole are linked together. Fractals are self-similar, as those parts are, at least approximately, scaled-down copies of the rough whole. In architecture, such a concept has also been known for a long time. Not only architects of the twentieth century called for an overall idea that is mirrored in every single detail, but also Gothic cathedrals and Indian temples offer self-similarity. This study mainly focuses upon the question whether this concept of self-similarity makes architecture with fractal properties more diverse and interesting than Euclidean Modern architecture. The first part gives an introduction and explains Fractal properties in various natural and architectural objects, presenting the underlying structure by computer programmed renderings. In this connection, differences between the fractal, architectural concept and true, mathematical Fractals are worked out to become aware of limits. This is the basis for dealing with the problem whether fractal-like architecture, particularly facades, can be measured so that different designs can be compared with each other under the aspect of fractal properties. Finally the usability of the Box-Counting Method, an easy-to-use measurement method of Fractal Dimension is analyzed with regard to architecture.
Fractal analysis: A new remote sensing tool for lava flows
NASA Technical Reports Server (NTRS)
Bruno, B. C.; Taylor, G. J.; Rowland, S. K.; Lucey, P. G.; Self, S.
1992-01-01
Many important quantitative parameters have been developed that relate to the rheology and eruption and emplacement mechanics of lavas. This research centers on developing additional, unique parameters, namely the fractal properties of lava flows, to add to this matrix of properties. There are several methods of calculating the fractal dimension of a lava flow margin. We use the 'structured walk' or 'divider' method. In this method, we measure the length of a given lava flow margin by walking rods of different lengths along the margin. Since smaller rod lengths transverse more smaller-scaled features in the flow margin, the apparent length of the flow outline will increase as the length of the measuring rod decreases. By plotting the apparent length of the flow outline as a function of the length of the measuring rod on a log-log plot, fractal behavior can be determined. A linear trend on a log-log plot indicates that the data are fractal. The fractal dimension can then be calculated from the slope of the linear least squares fit line to the data. We use this 'structured walk' method to calculate the fractal dimension of many lava flows using a wide range of rod lengths, from 1/8 to 16 meters, in field studies of the Hawaiian islands. We also use this method to calculate fractal dimensions from aerial photographs of lava flows, using lengths ranging from 20 meters to over 2 kilometers. Finally, we applied this method to orbital images of extraterrestrial lava flows on Venus, Mars, and the Moon, using rod lengths up to 60 kilometers.