Causes of the apparent scale independence of fractal indices associated with forest fragmentation in Bolivia

In a recent investigation, Landsat TM and ETM+ data were used to simulate different resolutions of remotely-sensed images (from 30 to 1100 m) and to analyze the effect of resolution on a range of landscape metrics associated with spatial patterns of forest fragmentation in Chapare, Bolivia since the mid-1980s. Whereas most metrics were found to be highly dependent on pixel size, several fractal metrics (DLFD, MPFD, and AWMPFD) were apparently independent of image resolution, in contradiction with a sizeable body of literature indicating that fractal dimensions of natural objects depend strongly on image characteristics. The present re-analysis of the Chapare images, using two alternative algorithms routinely used for the evaluation of fractal dimensions, shows that the values of the box-counting and information fractal dimensions are systematically larger, sometimes by as much as 85%, than the "fractal" indices DLFD, MPFD, and AWMFD for the same images. In addition, the geometrical fractal features of the forest and non-forest patches in the Chapare region strongly depend on the resolution of images used in the analysis. The largest dependency on resolution occurs for the box-counting fractal dimension in the case of the non-forest patches in 1993, where the difference between the 30 and I 100 m-resolution images corresponds to 24% of the full theoretical range (1.0 to 2.0) of the mass fractal dimension. The observation that the indices DLFD, MPFD, and AWMPFD, unlike the classical fractal dimensions, appear relatively unaffected by resolution in the case of the Chapare images seems due essentially to the fact that these indices are based on a heuristic, "non-geometric" approach to fractals. Because of their lack of a foundation in fractal geometry, nothing guarantees that these indices will be resolution-independent in general. (C) 2006 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Published by Elsevier B.V. All rights reserved.

Effect of tillage on fractal indices describing soil surface microrelief of a Brazilian Alfisol

Soil surface roughness is known to influence water infiltration, runoff and erosion. Soil surface roughness changes with management and weather and its mathematical description still remains an important issue. The main objective of this study was to investigate the effect of tillage on the two fractal indices, fractal dimension, D, and crossover length, 1, currently used in characterizing soil surface microrelief. The statistical index random roughness, RR, was also assessed. Field experiments were done on an Alfisol located at Rio Grande do Sul State (Brazil). Two tillage treatments (conventional versus direct drilling) were tested. The soil surface microrelief was assessed by point elevation measurements in 16 plots for each treatment. The sampling scheme was a square grid with 20 x 20 mm between point spacing and the plot size was 280 x 280 mm, so that each data set consisted of 225 individual elevation points. All indices were calculated after trend removal, both by slope correction, i.e., oriented microrelief, and by slope plus tillage marks correction, i.e., random microrelief. The implemented algorithm for estimating D and 1 consisted in evaluating the roughness around the local root mean square deviation (RMS) of the point elevation values. Irrespective of tillage treatment and detrending procedure, fractal behavior extended only over a bounded range of scales, from 40 to 100 mm, due to the experimental setup. In these conditions, assessing fractal indices was not always straightforward. The statistical index RR and the fractal index I were significantly different between tillage treatments for oriented and random surface conditions. D values of random soil surfaces were not affected by tillage treatment, whereas D values of oriented microrelief were significantly lower in the direct drilled plots. Removal of tillage marks trend resulted in a significant increase in D values. Within each tillage treatment, 1 and D were significantly correlated. (c) 2006 Elsevier B.V. All rights reserved.

Análise espaço temporal da dimensão fractal de matas ciliares na alta bacia do rio Passa Cinco - centro Leste do Estado de São Paulo

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

Fractal scaling exponents of heart rate variability association with linear indices and Poincaré Plot

The literature indicated that the fractal analysis of heart rate variability (HRV) is related to the chaos theory. However, it is not clear if the both short and long-term fractal scaling exponents of HRV are reliable for short period analysis in women. We evaluated the association of the fractal exponents of HRV with the time and frequency domain and geometric indices of HRV. We evaluated 65 healthy women between 18 and 30 years old. HRV was analyzed with a minimal number of 256 RR intervals in the time (SDNN, RMSSD, NN50 and pNN50) and frequency (LF, HF and LF/HF ratio) domains, the geometric index were also analyzed (triangular indexRRtri, triangular interpolation of RR intervals-TINN and Poincaré plot-SD1, SD2 and SD1/SD2) as well as short and long-term fractal exponents (alpha-1 and alpha-2) of the detrended fluctuation analysis (DFA). No significant correlation was observed for alpha-2 exponent with all indices. There was significant correlation of the alpha-1 exponent with RMSSD, pNN50, SDNN/RMSSD, LF (nu), HF (nu and ms2 ), LF/HF ratio, SD1 and SD1/SD2 ratio. Our data does not indicate the alpha-2 exponent to be used for 256 RR intervals and we support the alpha-1 exponent to be used for HRV analysis in this condition.

Fractal correlation of heart rate variability in obese children

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

Fractal correlation property of heart rate variability in chronic obstructive pulmonary disease

Background: It was reported that autonomic nervous system function is altered in subjects with chronic obstructive pulmonary disease (COPD). We evaluated short-and long-term fractal exponents of heart rate variability (HRV) in COPD subjects.Patients and methods: We analyzed data from 30 volunteers, who were divided into two groups according to spirometric values: COPD (n = 15) and control (n = 15). For analysis of HRV indices, HRV was recorded beat by beat with the volunteers in the supine position for 30 minutes. We analyzed the linear indices in the time (SDNN [standard deviation of normal to normal] and RMSSD [root-mean square of differences]) and frequency domains (low frequency [LF], high frequency [HF], and LF/HF), and the short-and long-term fractal exponents were obtained by detrended fluctuation analysis. We considered P < 0.05 to be a significant difference.Results: COPD patients presented reduced levels of all linear exponents and decreased short-term fractal exponent (alpha-1: 0.899 +/- 0.18 versus 1.025 +/- 0.09, P = 0.026). There was no significant difference between COPD and control groups in alpha-2 and alpha-1/alpha-2 ratio.Conclusion: COPD subjects present reduced short-term fractal correlation properties of HRV, which indicates that this index can be used for risk stratification, assessment of systemic disease manifestations, and therapeutic procedures to monitor those patients.

Fractal dynamics of heart rate variability for short term

The fractal analysis of heart rate variability (HRV) has been associated to the chaos theory. We evaluated the association of the fractal exponents of HRV with the time and frequency domain and geometric indices of HRV for short period. HRV was analyzed with a minimal number of 256 RR intervals in the time (SDNN-standard deviation of normal-to-normal R-R intervals, pNN50-percentage of adjacent RR intervals with a difference of duration greater than 50ms and RMSSD-root-mean square of differences between adjacent normal RR intervals in a time interval) and frequency (LF-low frequency, HF-high frequency and LF/HF ratio) domains. The geometric indexes were also analyzed (RRtri-triangular index, TINN-triangular interpolation of RR intervals and Poincaré plot) as well as short and long-term fractal exponents (alpha-1 and alpha-2) of the detrended fluctuation analysis (DFA). We observed strong correlation of the alpha-1 exponent with RMSSD, pNN50, SDNN/RMSSD, LF (nu), HF (nu), LF/HF ratio, SD1 and SD1/Sd2 ratio. In conclusion, we suggest that the alpha-1 exponent could be applied for HRV analysis with a minimal number of 256 RR intervals.

Fractal correlation property of heart rate variability in response to the postural change maneuver in healthy women

Background: We evaluated the effects of the PCM on the fractal analysis of the HRV in healthy women Method: We evaluated healthy women between 18 and 30 years old. HRV was analyzed in the time (SDNN, RMSSD, NN50 and pNN50) and frequency (LF, HF and LF/HF ratio) domains as well as short and long-term fractal exponents (alpha-1 and alpha-2) of the detrended fluctuation analysis (DFA). HRV was recorded at rest for ten minutes at seated rest and then the women quickly stood up from a seated position in up to three seconds and remained standing for 15 minutes. HRV was recorded at the following time: rest, 0–5 min, 5–10 min and 10–15 min during standing. Results: We observed decrease (p < 0.05) in the time-domain indices of HRV between seated and 10–15 minutes after the volunteer stood up. The LF (ms2) and HF (ms2) indices were also reduced (p < 0.05) at 10–15 minutes after the volunteer stood up compared to seated while the LF (nu) was increased at 5–10 min and 10–15 min (p < 0.05). The short-term alpha-1 exponent was increased (p < 0.05) at all moments investigated compared to seated. Increase in the properties of short-term fractal correlations of heart rate dynamics accompanied by a decrease in the parasympathetic modulation and global HRV was observed in response to the postural change maneuver. Conclusion: We suggest that fractal analysis of HRV is more sensitive than frequency and time-domain analysis of HRV during the postural change maneuver.

Comparison of fractal dimensions based on segmented NDVI fields obtained from different remote sensors.

Satellite image data have become an important source of information for monitoring vegetation and mapping land cover at several scales. Beside this, the distribution and phenology of vegetation is largely associated with climate, terrain characteristics and human activity. Various vegetation indices have been developed for qualitative and quantitative assessment of vegetation using remote spectral measurements. In particular, sensors with spectral bands in the red (RED) and near-infrared (NIR) lend themselves well to vegetation monitoring and based on them [(NIR - RED) / (NIR + RED)] Normalized Difference Vegetation Index (NDVI) has been widespread used. Given that the characteristics of spectral bands in RED and NIR vary distinctly from sensor to sensor, NDVI values based on data from different instruments will not be directly comparable. The spatial resolution also varies significantly between sensors, as well as within a given scene in the case of wide-angle and oblique sensors. As a result, NDVI values will vary according to combinations of the heterogeneity and scale of terrestrial surfaces and pixel footprint sizes. Therefore, the question arises as to the impact of differences in spectral and spatial resolutions on vegetation indices like the NDVI. The aim of this study is to establish a comparison between two different sensors in their NDVI values at different spatial resolutions.

Are European equity markets efficient? New evidence from fractal analysis

We report an empirical analysis of long-range dependence in the returns of eight stock market indices, using the Rescaled Range Analysis (RRA) to estimate the Hurst exponent. Monte Carlo and bootstrap simulations are used to construct critical values for the null hypothesis of no long-range dependence. The issue of disentangling short-range and long-range dependence is examined. Pre-filtering by fitting a (short-range) autoregressive model eliminates part of the long-range dependence when the latter is present, while failure to pre-filter leaves open the possibility of conflating short-range and long-range dependence. There is a strong evidence of long-range dependence for the small central European Czech stock market index PX-glob, and a weaker evidence for two smaller western European stock market indices, MSE (Spain) and SWX (Switzerland). There is little or no evidence of long-range dependence for the other five indices, including those with the largest capitalizations among those considered, DJIA (US) and FTSE350 (UK). These results are generally consistent with prior expectations concerning the relative efficiency of the stock markets examined. © 2011 Elsevier Inc.

Écoulements granulaires par avalanches : indices de fluidité, fractales et multifractales

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Écoulements granulaires par avalanches : indices de fluidité, fractales et multifractales

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Fractal descriptors for quantifying brain complexity in MRI

Magnetic Resonance Imaging (MRI) is the in vivo technique most commonly employed to characterize changes in brain structures. The conventional MRI-derived morphological indices are able to capture only partial aspects of brain structural complexity. Fractal geometry and its most popular index, the fractal dimension (FD), can characterize self-similar structures including grey matter (GM) and white matter (WM). Previous literature shows the need for a definition of the so-called fractal scaling window, within which each structure manifests self-similarity. This justifies the existence of fractal properties and confirms Mandelbrot’s assertion that "fractals are not a panacea; they are not everywhere". In this work, we propose a new approach to automatically determine the fractal scaling window, computing two new fractal descriptors, i.e., the minimal and maximal fractal scales (mfs and Mfs). Our method was implemented in a software package, validated on phantoms and applied on large datasets of structural MR images. We demonstrated that the FD is a useful marker of morphological complexity changes that occurred during brain development and aging and, using ultra-high magnetic field (7T) examinations, we showed that the cerebral GM has fractal properties also below the spatial scale of 1 mm. We applied our methodology in two neurological diseases. We observed the reduction of the brain structural complexity in SCA2 patients and, using a machine learning approach, proved that the cerebral WM FD is a consistent feature in predicting cognitive decline in patients with small vessel disease and mild cognitive impairment. Finally, we showed that the FD of the WM skeletons derived from diffusion MRI provides complementary information to those obtained from the FD of the WM general structure in T1-weighted images. In conclusion, the fractal descriptors of structural brain complexity are candidate biomarkers to detect subtle morphological changes during development, aging and in neurological diseases.

Comparing Near-infrared Conventional Diffuse Reflectance Spectroscopy And Hyperspectral Imaging For Determination Of The Bulk Properties Of Solid Samples By Multivariate Regression: Determination Of Mooney Viscosity And Plasticity Indices Of Natural Rubber.

Conventional reflectance spectroscopy (NIRS) and hyperspectral imaging (HI) in the near-infrared region (1000-2500 nm) are evaluated and compared, using, as the case study, the determination of relevant properties related to the quality of natural rubber. Mooney viscosity (MV) and plasticity indices (PI) (PI0 - original plasticity, PI30 - plasticity after accelerated aging, and PRI - the plasticity retention index after accelerated aging) of rubber were determined using multivariate regression models. Two hundred and eighty six samples of rubber were measured using conventional and hyperspectral near-infrared imaging reflectance instruments in the range of 1000-2500 nm. The sample set was split into regression (n = 191) and external validation (n = 95) sub-sets. Three instruments were employed for data acquisition: a line scanning hyperspectral camera and two conventional FT-NIR spectrometers. Sample heterogeneity was evaluated using hyperspectral images obtained with a resolution of 150 × 150 μm and principal component analysis. The probed sample area (5 cm(2); 24,000 pixels) to achieve representativeness was found to be equivalent to the average of 6 spectra for a 1 cm diameter probing circular window of one FT-NIR instrument. The other spectrophotometer can probe the whole sample in only one measurement. The results show that the rubber properties can be determined with very similar accuracy and precision by Partial Least Square (PLS) regression models regardless of whether HI-NIR or conventional FT-NIR produce the spectral datasets. The best Root Mean Square Errors of Prediction (RMSEPs) of external validation for MV, PI0, PI30, and PRI were 4.3, 1.8, 3.4, and 5.3%, respectively. Though the quantitative results provided by the three instruments can be considered equivalent, the hyperspectral imaging instrument presents a number of advantages, being about 6 times faster than conventional bulk spectrometers, producing robust spectral data by ensuring sample representativeness, and minimizing the effect of the presence of contaminants.

Influence of Urea and Ammonium Sulfate on Soil Acidity Indices in Lowland Rice Production

Urea and ammonium sulfate are principal nitrogen (N) sources for crop production. Two field experiments were conducted during three consecutive years to evaluate influence of urea and ammonium sulfate application on grain yield, soil pH, calcium (Ca) saturation, magnesium (Mg) saturation, base saturation, aluminum (Al) saturation, and acidity (H + Al) saturation in lowland rice production. Grain yield was significantly influenced by urea as well as ammonium sulfate fertilization. Soil pH linearly decreased with the application of N by ammonium sulfate and urea fertilizers. However, the magnitude of the pH decrease was greater by ammonium sulfate than by urea. The Ca and Mg saturations were decreased at the greater N rates compared to low rates of N by both the fertilizer sources. The Al and acidity saturation increased with increasing N rates by both the fertilizer sources. However, these acidity indices were increased more with the application of ammonium sulfate compared with urea. Rice grain yield had negative associations with pH, Ca saturation, Mg saturation, and base saturation and positive associations with Al and acidity saturation. This indicates that rice plant is tolerant to soil acidity.