Fractal Slope Research Articles

Fractal Slope-Based Seismic Wave Detection Method

ABSTRACT Automatic P-wave arrival detection is the first task in an earthquake early warning systems. This study proposes a novel detection method for this based on a fractal slope (FS). We improved the calculation method of the fractal dimension to increase the calculation speed and proposed a continuous algorithm. Furthermore, we applied FS in conjunction with the short-term average over the long-term average (STA/LTA), named STA/LTA + FS. We designed orthogonal experiments with different parameters and selected a total of 40,020 sets of seismic waves from the Japanese dataset to test the best parameters. A total of 45,302 sets of seismic waves from the STanford EArthquake dataset and the Chinese dataset were selected to test the generality of the proposed method. The results show that the mean error in detection time of the proposed method is +0.042 s for different datasets. In addition, STA/LTA + FS is robust over a wide range of signal-to-noise ratio, epicentral distance, and magnitude, with the percentage of timing errors below 0.5 s higher than 95%.

Application of spectral analysis and wavelet transforms to full-scale dynamic drainages at minesites

This paper focusses on the application of spectral analysis and continuous wavelet transforms to water drainages from full-scale minesite components, such as open pits, waste-rock piles, and tailings impoundments. Three minesite-drainage databases included high-frequency monitoring (as frequently as every 15 min) and/or long-term monitoring (up to 31 years) of both flows and aqueous chemistries. These databases were cleaned only by deleting very obvious outliers and ignoring statistical significance, so that extreme events and fractal patterns could be detected. In all three full-scale minesite-drainage databases, 1-over-f fractal slopes were common in the spectral analyses, but other slopes mostly between zero and 2.0 were also found. Spectral analyses also produced anomalous spectral slopes. Simple simulations showed these could be explained by major unseen seasonal changes in water retention by upstream buried ponds or subsurface aquitards. Wavelet transforms for the three minesite-drainage databases provided important observations such as (1) the varying strengths of periodicity with time, (2) the differing periodicities between physical drainage flows and their aqueous chemistries, and (3) the effect of placing a fine-grained soil/till cover over a waste-rock pile. Based on all three minesite-drainage databases, the most common wavelengths for strong, persistent periodicities were 1 year and 1 week. Other wavelengths of strong periodicity for at least two minesites were 10 years, approximately 4 months, and half-monthly to monthly. The minesite with data as frequent as every 15 min also showed strong periodicities over 1 day and less.

Robust Fetal Heart Beat Detection via R-Peak Intervals Distribution.

Monitoring fetal heart rate during pregnancy is essential to assist clinicians in making more timely decisions. Non-invasive monitoring of fetal heart activities using abdominal ECGs is useful for diagnosis of heart defects. However, the extracted fetal ECGs are usually too weak to be robustly detected. Thus, it is a necessity to enhance fetal R-peak since their peaks may be hidden within the signal due to the immaturity of the fetal cardiovascular system. Therefore, to improve the detection of the fetal heartbeat, a novel fetal R-peak enhancement technique was proposed to statistically generate the weighting mask according to the distribution of the neighboring temporal intervals between each pair of peaks. Two sets of simulations were designed to validate the reliability of the method: challenges with different levels of (1) noise contamination and (2) R-peak interval changing rate. The simulation results showed that the weighting mask improved the accuracy of the R-peak detection rate by 25% and decreased the false alarm rate by 20% with white noise contamination, and ensured high R-peak detection rate (>80%), especially with mild noise contamination (noise amplitude ratio <1.5 and noise rate per minute <25%). For the simulations with continuous R-peak intervals changing, the masking process can still effectively eliminate noise contamination especially when the amplitude of the sinusoidal fetal R-R intervals is lower than 50 ms. For the real fetus ECGs, the detection rate was increased by 3.498%, whereas the false alarm rate was decreased by 3.933%. Next, we implemented the fetal R-peak enhancement technique to investigate fractal regulation and multiscale entropy of the real fetal heartbeat intervals. Both scaling exponent (∼0.6 to ∼1 in scale 4-15) and entropy measure (scale 6-10) increased with gestational ages (22-40 weeks). The results confirmed fractal slope and complexity of fetal heartbeat intervals can reflect the maturation of fetus organism.

Evolution of erythrocytes aggregation: A fractal approach when incubated with Trichinella spiralis and Ascaris lumbricoides

Fil: Lupo, Maela. Consejo Nacional de Investigaciones Cientificas y Tecnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Bioquimicas y Farmaceuticas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Medicas; Argentina

Abstract 17013: Post-traumatic Stress Disorder is Associated with Adverse Non-Linear Heart Rate Variability in Veteran Twins

BACKGROUND: Veterans with post-traumatic stress disorder (PTSD) have higher risk of coronary heart disease (CHD) incidence and mortality. Psychological conditions may have an adverse effect on the autonomic nervous system, and may in part have genetic origins. Novel non-linear measures of heart rate variability (HRV), such as fractal dimension (FD) and power law slope have been associated with mortality and may signify autonomic dysfunction. We hypothesized that PTSD is associated with reduced FD and increased power law slope, suggesting higher mortality risk. METHODS: FD and power law slope were measured from 24-hour Holter recordings in 416 predominantly healthy middle-aged male twins from the Vietnam Era Twin Registry. Current (symptoms within the past month) and remitted (past history of) PTSD were measured using the Structured Clinical Interview for Psychiatry Disorders. Mixed-effect regression models were used to adjust for twin clustering and account for genetic/familial influences. RESULTS: The mean age was 56 ± 3 years, 35 had current PTSD, and 46 had remitted PTSD. In models that analyzed twins as individuals, current PTSD was significantly associated with 22% reduced FD and 18% increased power law slope. This association persisted for power law slope after adjustment for traditional risk factors, lifestyle factors, depression, and anti-depressant medication use (table). After controlling for genetic/familial factors by comparing twin brothers discordant for current PTSD within pairs (20 pairs), both measures remained significantly associated with current PTSD. Remitted PTSD did not influence HRV measures. No interaction by zygosity was found. CONCLUSIONS: Vietnam era veterans with PTSD have reduced FD and increased power law slope persisting after multivariable adjustment. This suggests that autonomic mechanisms, independent of genetic and familial effects, may contribute to increased CHD and mortality in veterans with PTSD.

Patients with Complex Regional Pain Syndrome Type 1

Patients with complex regional pain syndrome type 1 might have disturbed autonomic function and increased heart rate fractal dynamics with a resultant impaired baroreflex sensitivity (BRS). We hypothesized that these parameters of impaired cardiovascular regulation might improve with a reduction of pain intensity. Ten patients and 10 healthy volunteers entered the study. Power spectral analysis of heart rate (HR) variability was performed by the maximum entropy method. Ratios of low-frequency domain to high-frequency domain (LF/HF) and a fractal slope, the slope of a regression line of power spectral density (1/f), were calculated. BRS was assessed with a head-up tilt test. When the visual analogue scale scores decreased to ≤ 20 mm during treatments, those measurements were repeated. LF/HF and steepness of fractal slope before treatments decreased significantly during treatments when visual analogue scale was ≤ 20 mm (2.23 ± 0.68 to 1.30 ± 0.45, P=0.005 and -1.90 ± 0.35 to -1.16 ± 0.14, P=0.00032, respectively). BRS before treatments was low (-0.28 ± 0.27 bpm/mm Hg) as compared with BRS of volunteers but significantly improved to -0.62 ± 0.48 bpm/mm Hg during treatments (P=0.032). Increased LF/HF ratios likely indicate that patients had an imbalance of the autonomic nervous system. The increased fractal slope suggests that patients developed strong self-similarity of HR variability. The highly predictable HR variability leads to impaired hemodynamic homeostasis, resulting in decreased BRS. The impaired cardiovascular regulation improved with a reduction of pain. Thus, spectral analysis of HR variability may be useful objectively to follow complex regional pain syndrome type 1 patients, not only for pain management but also for the status of cardiovascular stability.

Fractal Cardiovascular Dynamics and Baroreflex Sensitivity After Stellate Ganglion Block

It has been shown that stellate ganglion block can attenuate baroreflex sensitivity. Our primary purpose in this study was to determine whether fractal dynamics (dynamic change of self-similar fluctuation patterns) of not only heart rate but also systolic blood pressure variability are involved in attenuation of baroreflex sensitivity after stellate ganglion block. Sixteen young, healthy volunteers entered the study. Spectral analysis of heart rate and systolic blood pressure variability was performed before and 30, 60, 90, and 120 min after either right or left stellate ganglion block, separated by a 1 to 1(1/2)-mo interval, with 6 mL of 1% mepivacaine. Shortly after each spectral analysis, baroreflex sensitivity was assessed with the head-up tilt test. Baroreflex sensitivity, assessed by the head-up tilt test, was significantly attenuated at 30 min after either right or left stellate ganglion block (1.26 +/- 0.18 to 0.46 +/- 0.08 bpm/mm Hg, P < 0.05 and 1.17 +/- 0.35 to 0.51 +/- 0.13 bpm/min, P < 0.01, respectively). Fractal slopes reflecting the degree of self-similarity of fluctuations were significantly increased at 30 min after either right or left stellate ganglion block (right stellate ganglion block--heart rate; -1.08 +/- 0.30 to -1.62 +/- 0.22, P < 0.01; right stellate ganglion block--systolic blood pressure; -1.30 +/- 0.80 to -2.40 +/- 0.80, P < 0.05; left stellate ganglion block--systolic blood pressure; -1.20 +/- 0.40 to -2.13 +/- 0.50, P < 0.05). Fractal slope did not change after left stellate ganglion block with heart rate variability analysis. Loss of complexity (status of being complex behavior) of both heart rate and systolic blood pressure variability, indicated by increased fractal slopes, is one mechanism in attenuating baroreflex sensitivity after stellate ganglion block.

Recovery of heart rate variability profile in patients after coronary artery surgery.

We examined the different characteristics of heart rate variability (HRV) to define the time course of HRV profile after coronary artery surgery (CAS). Spectral analysis of HRV was performed on a 512-s segment of R-R intervals of the electrocardiogram on the preoperative day and on Postoperative Days 1, 2, 3, 4, 5, 6, 7, 14, 21, and 28. Power spectral area was divided into low (0.04-0.15 Hz; LF)- and high (0.15-0.5 Hz; HF)-frequency components. Fractal slope and sympathovagal slope of 1/f characteristics of HRV were determined in two different frequency ranges (from 0.01 to 0.15 Hz and from 0.01 to 0.5 Hz, respectively). Three recovery profiles of HRV were identified. Early HRV recovery profiles (Postoperative Days 1-6) included reduction in LF, HF, and sympathovagal slope, as well as an increase in fractal slope. Subsequent HRV recovery profiles (Postoperative Days 7-21) revealed reductions in LF, HF, and sympathovagal slope. Fractal slope became normal. Later HRV recovery profiles (Postoperative Day 28) demonstrated that all spectral components of HRV remained reduced, but sympathovagal and fractal slopes became normal. These changes in the HRV profile after CAS suggest significant postoperative alterations in cardiovascular homeostasis with significant but incomplete recovery during the first 28 postoperative days. Heart rate variability reflects normal neural regulation of cardiac function. This variability remains depressed as long as 28 days after coronary artery bypass surgery, but can recover as early as 1 wk postoperatively. Despite implied loss of normal neural regulation of cardiac function, a specific correlation between depressed heart rate variability and outcomes was not performed.

Characterizing Multispectral Images of Tumorous, Bruised, Skin-torn, and Wholesome Poultry Carcasses

A multispectral imaging system which provides image information of poultry carcasses in the spatial and the frequency domains was developed. This article discusses the spectral image characterization of poultry carcasses for separating tumorous, bruised and skin-torn carcasses from the normal carcasses based on the gray-scale intensity, Fourier power spectrum, and fractal analyses of the spectral images. Tumorous, bruised, and other damaged carcasses were scanned by an intensified multispectral camera with various wavelength filters (542-847 nm). The results showed that the spectral images scanned at the optical wavelengths of 542 and 700 nm were useful for separating the tumorous from the normal carcasses in the spatial domain. Fractal dimension, roughness and slope were calculated from the Fourier spectra of each carcass. The mean fractal dimension of the normal carcasses scanned at 542 nm wavelength was larger than that of tumorous carcasses (P < 0.005) and skin-torn carcasses (P < 0.1). Fractal dimension of tumor (542 nm) was smaller than that of bruised carcasses of 542 nm spectral images (P < 0.01). The fractal slope mean values of the normal carcasses were larger than the tumor (P < 0.005) and the bruise (P < 0.05). Whereas, the slope of bruised carcass scanned at 542 nm was much smaller than the slope of bruise scanned at 700 nm (P < 0.005). Neural network classifier performed with 91.4% accuracy for the separation of tumorous carcasses from normals based on the spectral images scanned at both 542 and 700 nm wavelengths.

Evolution of the Structure Factor in Gelling Dense Colloidal Silica

ABSTRACTA solution of 30 % by mass, 7 nm diameter, colloidal silica spheres has been studied during gelation using small angle neutron scattering (SANS). A peak in the static structure factor appears early at a wavevector q ≈ 0.1 nm−1, and then grows in height and shifts to lower wavevectors as gelation proceeds. This is consistent with a cluster growth model in which this low-q peak in the structure factor indicates the presence of correlations between growing clusters. The peak continues to grow after the solution has visibly gelled indicating that the gel coarsens even after a stiff solid-like network has formed. The clear presence of cluster correlations at length scales only one order of magnitude larger than the particle size means that the usual fractal slope analyses are invalid in this system. We interpret the results by comparing the measured time evolution of the structure factor with computer simulations of Lennard-Jones particles quenched far below the critical line.

Scintillation in the Fresnel Region Behind a Sub-fractal Diffuser

The results of a numerical computation of contrast versus propagation distance in the Fresnel region behind a diffuser with fractal slope are presented and discussed. Both corrugated and isotropic cases are examined for a range of values of the diffuser spectral index and it is found that, in the absence of a finite outer scale, the asymptotic value of the contrast at large distances is greater than that of gaussian speckle. The contrast plot is monotonic for ‘smoother’ scatterers but develops a weak peak as the fractal/sub-fractal marginal case is approached. The effect of a finite outer scale is examined briefly, and a comparison is made with published experimental data.

Fraunhofer Scattering by a Sub-fractal Diffuser

It is shown that the contrast of the far-field intensity pattern, generated by illuminating a small area of a gaussian random diffuser with fractal slope, exhibits a characteristic power-law dependence on illuminated area.

Fresnel scattering by a corrugated random surface with fractal slope

Consideration of the density of rays emanating from an infinite, corrugated Gaussian surface with fractal slope reveals a hitherto unexplored shortwave scattering regime that is uncomplicated by the presence of caustics in the scattered wave field. The statistical and coherence properties of the ray-density fluctuations in this regime are calculated as a function of fractal dimension D, and it is shown that in the Brownian case (D = 1.5) the problem can be solved exactly. The properties of the intensity pattern in a coherent scattering configuration are also investigated. The contrast of the pattern is computed as a function of propagation distance, and the asymptotic behavior in the strong scattering limit is again found to be exactly solvable when D = 1.5. It is shown that the intensity fluctuations are K distributed in this case. The effects of a finite outer-scale size are evaluated and discussed.

Scattering by a corrugated random surface with fractal slope

The single-fold statistics of rays emanating from an infinite, corrugated Gaussian surface with fractal slope are investigated. Low moments of the ray-density fluctuation distribution are evaluated as a function of fractal dimension, D. It is shown that in the Brownian case, D=1.5, the distribution is exactly negative exponential, corresponding to K-distributed intensity fluctuations in a coherent scattering configuration.