Fractal Values Research Articles

Geo-ecological approach to evaluation of ecological condition of water bodies

The paper proposes a new approach to evaluation of ecological condition of water bodies. The method is based on the use of fractal dimension of the temporal dynamics of water environment pollution components as a quality indicator of state dynamics for a specific type of pollution or an ecosystem in its entirety. The method enables both common integrated and component-based differential evaluation. The writers have identified fractal threshold values that describe the extent of environmental stability of a water system, its resistance to industrial pollution, and probability of further anthropogenic loads. The paper offers a methodology to forecast the ecological condition of water bodies on the basis of quantitative estimation of dynamic fractal parameters representing pollution dynamics of water system components.

Fractal Characteristics of Geomorphology Units as Bouguer Anomaly Manifestations in Bumiayu, Central Java, Indonesia

Bumiayu in Central Java, Indonesia, has a typical landform characteristics. Differences of topography on each geomorphological unit indicated by the value of fractal dimension. This research provides important information on the influence of geomorphology conditions and subsurface geological phenomenon of research area based on fractal application. This research methodology relies on laboratory analysis and field observation. Landform is a characteristics of Bouguer anomaly contour manifestation. It is indicated by occurences of significant correlation between the Bouguer anomaly countour and geological cross section as well topography contour slope and Bouguer anomaly contour slope. Based on spatial analysis, morphology of research area is dominated by very high steep hills (more than 60%). Result of Bouguer anomaly countour analysis also shows that research area dominated by very high steep hills (more than 55%). Statistical analysis between the fractal value of lineament in Digital Elevation Model and fractal value of lineament in Bouguer anomaly countour as well the fractal value of topography countour and fractal value of Bouguer anomaly countour shows that the relationship was not significant. Further, the entire result of this verified research shows clearly that geomorphology conditions represents subsurface geological phenomenon.

Heart rate variability and insulin resistance among obese males

Heart rate variability analysis provides quantitative information about vagal and sympathetic modulation of cardiac function. To analyze the relationship between heart rate variability and insulin resistance in obese patients. Male participants were studied, divided in 10 obese subjects aged 27 ± 2 years with a body mass index (BMI) of 31.2 ± 1.3 kg/m², 15 overweight subjects aged 24 ± 3 years with a BMI of 26.7 ± 1.5 kg/m² and 14 normal weight subjects aged 21 ± 2 years with a BMI of 22.5 ± 1.3 kg/m². Resting heart rate variability was measured in a period of 5 minutes. A spectral analysis was done measuring the low frequency/high frequency ratio (LF/HF). A non- linear analysis was carried out measuring the standard deviation of the instantaneous variation of RR intervals (SD1) and α-1 or a fractal analysis of RR interval complexity. A fasting blood sample was obtained to measure blood glucose and insulin and calculate the homeostasis model assessment for insulin resistance (HOMA-IR). Among obese subjects HOMA-IR, LF/HF, α-1 and SD1 values were 2.6 ± 2.1, 2.4 ± 1.8, 1.2 ± 0.06 and 22.5 ± 10 respectively. The figures for normal weight subjects were 0.5 ± 0.1, 1.3 ± 0.2, 0.9 ± 0.3 and 26 ± 7.8 respectively. There is an association between spectral and fractal values of heart rate variability and HOMA-IR. These results may indicate a predominance of sympathetic control of heart rate among obese subjects.

Physical features, phenolic compounds, betalains and total antioxidant capacity of coloured quinoa seeds (Chenopodium quinoa Willd.) from Peruvian Altiplano

Physical features, bioactive compounds and total antioxidant capacity (TAC) of coloured quinoa varieties (Chenopodium quinoa Willd.) from Peruvian Altiplano were studied. Quinoa seeds did not show a pure red colour, but a mixture which corresponded to different fractal colour values (51.0–71.8), and they varied from small to large size. Regarding bioactive compounds, total phenolic (1.23–3.24mg gallic acid equivalents/g) and flavonol contents (0.47–2.55mg quercetin equivalents/g) were highly correlated (r=0.910). Betalains content (0.15–6.10mg/100g) was correlated with L colour parameter (r=−0.569), total phenolics (r=0.703) and flavonols content (r=0.718). Ratio of betaxanthins to betacyanins (0.0–1.41) was negatively correlated with L value (r=−0.744). Whereas, high TAC values (119.8–335.9mmol Trolox equivalents/kg) were negatively correlated with L value (r=−0.779), but positively with betalains (r=0.730), as well as with free (r=0.639), bound (r=0.558) and total phenolic compounds (r=0.676). Unexploited coloured quinoa seeds are proposed as a valuable natural source of phenolics and betalains with high antioxidant capacity.

Study of the Influence of the Deep-Water Channel Project in the Yangtze River Estuary on Ecological Landscape and Fractal Dimensions of Jiuduan Shoal Tidal Channels

Chen, L. and Han, Z., 2015. Study of the influence of the deep-water channel project in the Yangtze River estuary on ecological landscape and fractal dimensions of Jiuduan Shoal tidal channels.The Jiuduan Shoal has the most extensive tidal channel system in the Yangtze River estuary diara, and the construction of the Deep-Water Channel Project in the Yangtze River estuary has had a significant effect on the distribution and morphology of tidal channels. Taking tidal channels in the Jiuduan Shoal in Yangtze River estuary as a research object, using remote sensing data which was extracted from 1997 to 2013, we analyzed the influence of the Deep-Water Channel Project in the Yangtze River estuary on the ecological landscape of Jiuduan Shoal tidal channels by using landscape indexes such as Total Class Area (CA), Number of Patches (NP), Patch Density (PD), Percentage of Landscape (PLAND), Landscape Shape Index (LSI), Fractal Dimension Index (FRAC), and Largest Patch Index (LPI). Graded tidal channels by using the principle of Horton Strahler of image of 2013. We found that, in the 1st and the 2nd phase of the project, the proportion of the tidal channel area increased compared to the previous period, but by the end of the 2nd phase project in 2013, the proportion of the total landscape area made up of tidal channels accounted for less in successive years; NP, PD, LSI, and LPI fluctuated in the first phase of Deep-Water Channel Project, after this tidal channels of Jiuduan Shoal maintained the same trend, namely, the tidal channels aggregation degree decreased year by year. The distribution of tidal channels tended toward separation which shows that the tidal channels fragmentation is increasing year by year. By the end of the third phase of construction, the shape of the tidal channels became gradually different and tended to be more discrete. The shape complexity increased and the tidal channels became more and more mature and complicated and can be seen in the same grade of Jiuduan Shoal tidal channels, which on the left side of the dimensions change range are greater than the right, namely, the tidal channels on the left side are more complex than the right. In different grades of of tidal channels, the change range of the minimum width is little, but the maximum is quite large. There is little relevance between the changes in the width of the different grades of tidal channels and its fractal dimension difference values between the left and right sides. In different grades of tidal channels, whether left or right, the fractal dimension values increase with the average width and grade number of tidal channels.

FRACTAL ASPECTS OF MISCIBLE DISPLACEMENT IN ROUGH FRACTURES: AN EXPERIMENTAL APPROACH

Experiments were performed to study the effect of fracture surface roughness on fluid distribution during miscible displacement. The transparent replicas of single fractures obtained from seven different rocks were prepared and the surface roughness of each sample was described by fractal dimensions using the variogram, power spectral, and triangular prism (TP) techniques. Then, the effect of flow rate and viscosity on the geometry of the displacement front during miscible radial injection was investigated experimentally. The fractal dimensions of the fronts were obtained using box counting fractal analysis at different time lapses. The fractal values of invasion front varied from lithology to lithology, due to different surface roughnesses controlled by the lithology of the rocks. Although fluctuations of fractal values were observed during the growth of the front, fractal dimensions typically yielded an increasing trend. Fractal dimension became more stable with increasing flow rate and developed modestly with increasing viscosity. Finally, relationships between the fractal dimensions of displacement fronts and fracture surfaces were quantitatively analyzed and correlated in order to improve the prediction of fluid distribution within a single fracture during miscible displacement. Overall, correlations were observed between the surface characteristics and front fractal dimension values with some exceptions. In summary, to determine the probable distribution of miscible fluid and development of the front, all parameters except power spectral density (PSD) fractal dimension can be applied in the case of high viscosity ratios. In the case of low injection rates, TP could be applicable. No fractal behavior was present at extreme injection and low viscosity ratios, thus no correlation can be determined for the miscible displacement.

Fractal Structure of Au Geochemical Field for Shuikoushan Orefield in Hunan Province, China and its Application to Mineralization

The fractal measure on Au geochemical field of Mawangtang and Xinmengshan in Shuikoushan Pb-Zn-Au polymetallic ore field, Hunan, China was achieved by projective covering method in this paper. The results show a bifractal relation for Au Geochemical field which includes a textural fractal dimension (D1) at small scale and a structural fractal dimension (D2) at large scale with average breakpoint 86.0m which may be look as the movement scale of ore-forming fluid. All of fractal dimensions were between 2 to 3, D1 was 2.0011 and D2 was 2.0001 at Mawangtang as well as D1 was 2.4466 and D2 was 2.0408 at Xinmengshan respectively. The fractal dimensions appear the textural fractal dimensions were larger than their structural fractal dimensions indicate that the evolution of ore-forming fluid more complex than background value of this ore field. And what’s more, the fractal values of Mawangtang were larger than Xinmengshan may result from the mineralization with the former not only control by the overthrust structure and fold the same as the latter but also had a closed relationship with the acid to mafic magmatism.

Fractal boundary value problems for integral and differential equations with local fractional operators

In the present paper we investigate the fractal boundary value problems for the Fredholm\Volterra integral equations, heat conduction and wave equations by using the local fractional decomposition method. The operator is described by the local fractional operators. The four illustrative examples are given to elaborate the accuracy and reliability of the obtained results.

Variable Data-Flow Graph for Lightweight Program Slicing and Visualization

To understand the behavior of a program, developers often need to read source code fragments in various modules. Systemdependence-graph-based (SDG) program slicing is a good candidate for supporting the investigation of data-flow paths among modules, as SDG is capable of showing the data-dependence of focused program elements. However, this technique has two problems. First, constructing SDG requires heavyweight analysis, so SDG is not suitable for daily uses. Second, the results of SDG-based program slicing are difficult to visualize, as they contain many vertices. In this research, we proposed variable dataflow graphs (VDFG) for use in program slicing techniques. In contrast to SDG, VDFG is created by lightweight analysis because several approximations are used. Furthermore, we propose using the fractal value to visualize VDFG-based program slice in order to reduce the graph complexity for visualization purposes. We performed three experiments that demonstrate the accuracy of VDFG program slicing with fractal value, the size of a visualized program slice, and effectiveness of our tool for source code reading. key words: Static Analysis, Program Slicing, Variable Data-Flow Graph, Visualization

道路網形態のフラクタル次元と救急搬送に基づく実態圏域との相関

This study aimed to construct an evaluation technique by visualizing the existing area and setting of a road network by fractal dimension analysis to form the basis for road maintenance and improvement standards, and operating efficiency. As a criterion for protection of life, the initiation time of the treatment is considered an appraisal standard, and the numerical fractal value is shown to have a relationship with emergency medical transport.

Centre of Pressure Detection and Analysis with a High-resolution and Low-cost Smart Insole

This study aims to compare the accuracy of a pair of novel low-cost insoles with that of the proven standard Kistler force plate. The correlation of both devices had a r2 value of 0.942 and 0.946 for COPx and COPy respectively during dynamic tests conducted to measure macroscopic changes of the COP. Fractal dimension analysis was conducted to measure minute changes during quiet standing on solid surface and on foam, with both insoles and the force plate showing the same trend where the fractal values of standing on foam were significantly higher than that of standing on a solid surface. Further validation was done to compare the results with the mean velocities of the measured data that showed identical significant trends as the fractal dimension analysis.

Fractal Boundary Value Problems for Integral and Differential Equations with Local Fractional Operators

Fractal Boundary Value Problems for Integral and Differential Equations with Local Fractional Operators

Fractal characteristics of cracks and fragments generated in unloading rockburst tests

True triaxial rockburst experiments with four different unloading rates were performed on four prism specimens of granite sampled from Beishan, China. The damage evolution in the rockburst test was investigated from two aspects including fracture surface crack and fragment characteristics. The scanning electron microscopy was used to observe the micro crack information on fragment surface. Combing binarization and box counting dimensions, the fractal dimensions of cracks were obtained. Meanwhile, the fragments were collected and a sieving experiment was conducted. We weighed the fragments qualities, counted the amount of fragments and measured the fragments length, width and thickness. Utilizing four methods to calculate damage fractal dimensions of fragments, the trend of fractal value changing with unloading rates can be roughly described. It can be concluded from these experiments that the fractal dimension either for crack or for fragment holds a decreasing trend with the decreasing unloading rate, indicating a reduction of damage level.

Evaluation of cress seed gum and xanthan gum effect on macrostructure properties of gluten-free bread by image processing

In recent times computer vision employing image processing techniques has been developed rapidly in order to quantitatively characterize of foods. In this study, effect of cress seed gum as a novel gluten substitute and xanthan gum (1 % base on flour and starch weight) on gluten-free bread were investigated by image processing. Additionally, bread crumb analyzed during storage (24 and 72 h). Bread features selected for analysis were moisture content, specific volume, slice shape, crust and crumb color, pore area fraction, pore size distribution, number of cells/cm2, pore shape, fractal dimension of pore boundaries and crumb texture. The results exhibited, hydrocolloids improved quality of gluten-free breads significantly (p < 0.05). Hydrocolloid addition increased pore area fraction and had positive effect on crumb color during storage. Hydrocolloid by forming thick layer influenced the stability of gas cells and caused more regular and solids pores in gluten-free bread which was more noticeable in breads containing cress seed gum. Fractal values of boundaries indicated that the breads containing cress seed gum had more regular and smooth boundaries. Texture analysis by gray level co-occurrence matrix revealed stability crumb texture during storage.

Fractals and self-organized criticality in proteins

Self-organized criticality, a powerful concept, originated in 1987 as an extension of fractal geometries to thermodynamic systems in the vicinities of instabilities. The value of fractal methods can be greatly enhanced in realistic models that exploit accurate fractal values derived from homogeneous (possibly curated) Big Data. We illustrate this point by discussing the derivation of fractal exponents describing protein–water interactions, and their application to protein roughness, protein binding and potentially protein engineering. The examples studied are evolution of lysozyme c and acylphosphatase, and mutational effects on their aggregation.

Surface Roughness Characterization of ZnO: TiO2-Organic Blended Solar Cells Layers by Atomic Force Microscopy and Fractal Analysis

The objective of this work is to quantitatively characterize the 3D complexity of ZnO : TiO 2-organic blended solar cells layers by atomic force microscopy and fractal analysis. ZnO : TiO 2-organic blended solar cells layers were investigated by AFM in tapping-mode in air, on square areas of 25 μm2. A detailed methodology for ZnO : TiO 2-organic blended solar cells layers surface fractal characterization, which may be applied for AFM data, is presented. Detailed surface characterization of the surface topography was obtained using statistical parameters, according with ISO 25178-2: 2012. The fractal dimensions Df values (all with average ± standard deviation), obtained with morphological envelopes method, for: blend D1 ( P 3 HT : PCBM : ZnO : TiO 2 blend with ratio 1:0.35:0.175:0.175 mg in 1 ml of Chlorobenzene) is Df = 2.55 ± 0.01; and for blend D2 ( P 3 HT : PCBM : ZnO : TiO 2 blend with ratio 1:0.55:0.075:0.075 mg in 1 ml of Chlorobenzene) is Df = 2.45 ± 0.01. Denoting the ratios in 1 ml of Chlorobenzene with D1 and D2 articles. The 3D surface roughness of samples revealed a fractal structure at nanometer scale. Fractal and AFM analysis may assist manufacturers in developing ZnO : TiO 2-organic blended solar cells layers with better surface characteristics and provides different yet complementary information to that offered by traditional surface statistical parameters.

Fractal analysis of shape changes in murine osteoblasts cultured under simulated microgravity

Morphological changes have been reported to occur in cells exposed to microgravity, even if quantitative (i.e., fractal) analysis has been never performed on cell shape. We investigated cell shape as well as cytoskeleton modifications induced by simulated microgravity on murine osteoblasts (MC3T3-E1) growing in vitro by means of fractal analysis. On average, after 48–72 h of exposition to microgravity, osteoblasts display significant changes in shape profile, recovering a more rounded phenotype characterized by larger surface area than controls. More specifically, microgravity enacted the emergence of two distinct morphological phenotypes, one of which characterized by an increase in membrane fractal values, surface area, and roundness. Moreover, osteoblasts exposed to microgravity undergo significant functional changes (inhibited growth proliferation, increased apoptosis, β1-integrin decrease, impaired Akt and Erk phosphorylation) that could likely concur in explaining the observed alteration in bone structure experienced by astronauts.

Phenotypic Switch Induced by Simulated Microgravity on MDA-MB-231 Breast Cancer Cells

Microgravity exerts dramatic effects on cell morphology and functions, by disrupting cytoskeleton and adhesion structures, as well as by interfering with biochemical pathways and gene expression. Impairment of cells behavior has both practical and theoretical significance, given that investigations of mechanisms involved in microgravity-mediated effects may shed light on how biophysical constraints cooperate in shaping complex living systems. By exposing breast cancer MDA-MB-231 cells to simulated microgravity (~0.001 g), we observed the emergence of two morphological phenotypes, characterized by distinct membrane fractal values, surface area, and roundness. Moreover, the two phenotypes display different aggregation profiles and adherent behavior on the substrate. These morphological differences are mirrored by the concomitant dramatic functional changes in cell processes (proliferation and apoptosis) and signaling pathways (ERK, AKT, and Survivin). Furthermore, cytoskeleton undergoes a dramatic reorganization, eventually leading to a very different configuration between the two populations. These findings could be considered adaptive and reversible features, given that, by culturing microgravity-exposed cells into a normal gravity field, cells are enabled to recover their original phenotype. Overall these data outline the fundamental role gravity plays in shaping form and function in living systems.

Analysis of trabecular bone using site-specific fractal values calculated from cone beam CT images

Objective The purpose of the study was to explore the use of cone beam CT (CBCT) images to calculate fractal values of trabecular bone.

Fractal continuum model for tracer transport in a porous medium

A model based on the fractal continuum approach is proposed to describe tracer transport in fractal porous media. The original approach has been extended to treat tracer transport and to include systems with radial and uniform flow, which are cases of interest in geoscience. The models involve advection due to the fluid motion in the fractal continuum and dispersion whose mathematical expression is taken from percolation theory. The resulting advective-dispersive equations are numerically solved for continuous and for pulse tracer injection. The tracer profile and the tracer breakthrough curve are evaluated and analyzed in terms of the fractal parameters. It has been found in this work that anomalous transport frequently appears, and a condition on the fractal parameter values to predict when sub- or superdiffusion might be expected has been obtained. The fingerprints of fractality on the tracer breakthrough curve in the explored parameter window consist of an early tracer breakthrough and long tail curves for the spherical and uniform flow cases, and symmetric short tailed curves for the radial flow case.