Topological properties and fractal analysis of a recurrence network constructed from fractional Brownian motions

Many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks. In this work, we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional Brownian motions (FBMs). First, our results indicate that the constructed recurrence networks have exponential degree distributions; the average degree exponent 〈λ〉 increases first and then decreases with the increase of Hurst index H of the associated FBMs; the relationship between H and 〈λ〉 can be represented by a cubic polynomial function. We next focus on the motif rank distribution of recurrence networks, so that we can better understand networks at the local structure level. We find the interesting superfamily phenomenon, i.e., the recurrence networks with the same motif rank pattern being grouped into two superfamilies. Last, we numerically analyze the fractal and multifractal properties of recurrence networks. We find that the average fractal dimension 〈dB〉 of recurrence networks decreases with the Hurst index H of the associated FBMs, and their dependence approximately satisfies the linear formula 〈dB〉≈2-H, which means that the fractal dimension of the associated recurrence network is close to that of the graph of the FBM. Moreover, our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks, and the multifractality of these networks becomes stronger at first and then weaker when the Hurst index of the associated time series becomes larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst index H=0.5 possesses the strongest multifractality. In addition, the dependence relationships of the average information dimension 〈D(1)〉 and the average correlation dimension 〈D(2)〉 on the Hurst index H can also be fitted well with linear functions. Our results strongly suggest that the recurrence network inherits the basic characteristic and the fractal nature of the associated FBM series.

Fractal analysis of bone texture : a screening tool for stress fracture risk?

Background The aim of this study was to identify specific bone characteristics of stress fracture (SF) cases in sportswomen. To date, no tool is able to distinguish individuals who are at risk, limiting preventive measures.

Material and methods We investigated the skeletal system of sportswomen who did sustain SF in the past (n = 19) and compared it with that of female controls (C) with a similar sporting history but without any fracture history (n = 20).

Bone mass and body composition were measured using dual-energy X-ray absorptiometry. Bone micro-architecture was investigated by calcaneal ultrasound and fractal analysis of calcaneus radiographic images. Oestradiol levels were measured by E.I.A, and IGF-1 by R.I.A. Menstrual characteristics, nutrient intake, and training were assessed using questionnaires.

Results The result of the fractal analysis, expressed by the Hmean parameter, was significantly lower in the SF group, reflecting a more complex structure of the trabecular micro-architectural organization (P < 0·005). Body mass index (BMI) at birth was also found to be lower in the SF cases as compared with their C (P < 0·03).

Multivariate analysis revealed that the fractal parameter Hmean, bone mineral content (BMC) at Ward's triangle and the BMI at birth correctly assigned 84·85% of the female athletes into their respective SF or C groups (P = 0·001).

Conclusion These results suggest that the fractal parameter and the BMI at birth may be able to identify female athletes most at risk for this overuse bone injury, as their low indexes might reflect a greater skeletal sensitivity.

Fractal analysis of leaf-texture properties as a tool for taxonomic and identification purposes: a case study with species from Neotropical Melastomataceae (Miconieae tribe)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fractal analysis of eroded surfaces by digital image processing

Jet impingement erosion test rig has been used to erode titanium alloy specimens (Ti-4Al-4V). Eroded surface profiles have been obtained by vertical sectioning method for light microscopy observation. Mixed fractals have been measured from profile images by a digital image processing and analysis technique. The use of this technique allows glimpsing a quantitative correlation among material properties, fractal surface topography and erosion phenomena. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Fractal analysis along stretch zone for an aluminum alloy

The topography of fracture surface along stretch zone front for Al7050 is analyzed about its fractal behavior and compared against local distributions of microstructural parameters and stretch zone height, considered here as a toughness parameter. Major influence on microscale was presented by precipitation density. Larger grains should be significant on topographic behavior at macroscale, besides the local toughness measured along stretch zone. The large scattering of fractal measurements along specimen width should limit the validity of models relating fractal values and fracture toughness. It is proposed that models based on mixed fractals must also consider some dispersion parameter instead of mean fractal measurements due to the overall complexity of fracture relief formation. It is suggested that sampling for fractal measurement must be restricted to plane strain region along fracture surface, due to smaller scattering in this region. (C) 2004 Elsevier B.V. All rights reserved.

3-D reconstruction by extended depth-of-field in failure analysis - Case study II: Fractal analysis of interlaminar fracture in carbon/epoxy composites

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bioglass Associated With Leukocyte-Poor Platelet-Rich Plasma in the Rabbit Maxillary Sinus: Histomorphometric, Densitometric, and Fractal Analysis

The objective of the present study was to evaluate the outcomes of autogenous bone graft (AB) and bioglass (BG) associated or not with leukocyte-poor platelet-rich plasma (LP-PRP) in the rabbit maxillary sinus (MS) by histomorphometric and radiographic analysis. Twenty rabbits divided into 2 groups (G1, G2) were submitted to sinus lift surgery. In G1, 10 MS were grafted with AB and 10 MS were grafted with BG. In G2, 10 MS were grafted with AB + LP-PRP and 10 MS were grafted with BG + LP-PRP. After 90 days, the animals were killed and specimens were obtained, x-rayed, and submitted to histomorphometric, radiographic bone density (RD) and fractal dimension analysis. Radiographic bone density mean values (SD), expressed as aluminum equivalent in mm, of AB, BG, AB + LP-PRP, and BG + LP-PRP groups were 1.79 (0.31), 2.04 (0.39), 1.61 (0.28), and 1.53 (0.30), respectively. Significant differences (P < 0.05) were observed between BG and AB, and BG + PRP and BG. Fractal dimension mean values were 1.48 (0.04), 1.35 (0.08), 1.44 (0.04), and 1.44 (0.06), respectively. Significant differences were observed between BG and AB, and AB + LP-PRP and BG. Mean values for the percentage of bone inside MS were 63.30 (8.60), 52.65 (10.41), 55.25 (7.01), and 51.07 (10.25), respectively. No differences were found. No correlations were observed among percentage of bone, RD and FD. Histological analysis showed that MS treated with AB presented mature and new bone formation. The other groups showed minor bone formation. Within the limitations of this study, the results indicated that at a 90-day time end point, AB yielded better results than AB + LP-PRP, BG, and BG + LP-PRP and should be considered the primary material for MS augmentation.

Probing the anomalous extinction of four young star clusters: the use of colour-excess, main-sequence fitting and fractal analysis

Aims. We studied four young star clusters to characterise their anomalous extinction or variable reddening and asses whether they could be due to contamination by either dense clouds or circumstellar effects. Methods. We evaluated the extinction law (R-V) by adopting two methods: (i) the use of theoretical expressions based on the colour-excess of stars with known spectral type; and (ii) the analysis of two-colour diagrams, where the slope of the observed colour distribution was compared to the normal distribution. An algorithm to reproduce the zero-age main-sequence (ZAMS) reddened colours was developed to derive the average visual extinction (A(V)) that provides the closest fit to the observational data. The structure of the clouds was evaluated by means of a statistical fractal analysis, designed to compare their geometric structure with the spatial distribution of the cluster members. Results. The cluster NGC 6530 is the only object of our sample affected by anomalous extinction. On average, the other clusters suffer normal extinction, but several of their members, mainly in NGC 2264, seem to have high R-V, probably because of circumstellar effects. The ZAMS fitting provides A(V) values that are in good agreement with those found in the literature. The fractal analysis shows that NGC 6530 has a centrally concentrated distribution of stars that differs from the substructures found in the density distribution of the cloud projected in the A(V) map, suggesting that the original cloud was changed by the cluster formation. However, the fractal dimension and statistical parameters of Berkeley 86, NGC 2244, and NGC 2264 indicate that there is a good cloud-cluster correlation, when compared to other works based on an artificial distribution of points.

Fractal analysis of laplacian pyramidal filters applied to segmentation of soil images

The laplacian pyramid is a well-known technique for image processing in which local operators of many scales, but identical shape, serve as the basis functions. The required properties to the pyramidal filter produce a family of filters, which is unipara metrical in the case of the classical problem, when the length of the filter is 5. We pay attention to gaussian and fractal behaviour of these basis functions (or filters), and we determine the gaussian and fractal ranges in the case of single parameter ?. These fractal filters loose less energy in every step of the laplacian pyramid, and we apply this property to get threshold values for segmenting soil images, and then evaluate their porosity. Also, we evaluate our results by comparing them with the Otsu algorithm threshold values, and conclude that our algorithm produce reliable test results.

Characterization of rock joints by fractal analysis

From a physical perspective, a joint experiences fracturing processes that affect the rock at both microscopic and macroscopic levels. The result is a behaviour that follows a fractal structure. In the first place, for saw-tooth roughness profiles, the use of the triadic Koch curve appears to be adequate and by means of known correlations the JRC parameter is obtained from the angle measured on the basis of the height and length of the roughnesses. Therefore, JRC remains related to the geometric pattern that defines roughness by fractal analysis. In the second place, to characterise the geometry of irregularities with softened profiles, consequently, is proposed a characterisation of the fractal dimension of the joints with a circumference arc generator that is dependent on an average contact angle with regard to the mid-plane. The correlation between the JRC and the fractal dimension of the model is established with a defined statistical ratio.