Fractal Correlation Research Articles

Effect of Pursed-Lip Breathing in Patients With COPD: Linear and Nonlinear Analysis of Cardiac Autonomic Modulation

Objective: The aim of the present study was to evaluate the effect of pursed-lip breathing (PLB) on cardiac autonomic modulation in individuals with chronic obstructive pulmonary disease (COPD) while at rest. Methods: Thirty-two individuals were allocated to one of two groups: COPD (n = 17; 67.29 ± 6.87 years of age) and control (n = 15; 63.2 ± 7.96 years of age). The groups were submitted to a two-stage experimental protocol. The first stage consisted of the characterization of the sample and spirometry. The second stage comprised the analysis of cardiac autonomic modulation through the recording of R-R intervals. This analysis was performed using both nonlinear and linear heart rate variability (HRV). In the statistical analysis, the level of significance was set to 5% (p ≤ 0.05). Results: PLB promoted significant increases in the SD1, SD2, RMSSD and LF (ms2) indices as well as an increase in α1 and a reduction in α2 in the COPD group. A greater dispersion of points on the Poincaré plots was also observed. The magnitude of the changes produced by PLB differed between groups. Conclusion: PLB led to a loss of fractal correlation properties of heart rate in the direction of linearity in patients with COPD as well as an increase in vagal activity and impact on the spectral analysis. The difference in the magnitude of the changes produced by PLB between groups may be related to the presence of the disease and alterations in the respiration rate.

Characterization of chaotic multiscale features on the time series of melt index in industrial propylene polymerization system

The chaos characteristics of melt index have been first explored, and the Hilbert–Huang transform method and time delay embedding method are applied to multiscale dynamic analysis on the time series of the melt index (MI) in the propylene polymerization industry. The research results show that the embedding delay is 2, the embedding dimension is 5, the correlation dimension D2 is 1.57, and the maximum Lyapunov exponent is 0.143 for the melt index series, which provide clear evidence of chaotic multiscale features in the propylene polymerization process. Three intrinsic mode functions (IMFs) are decomposed from the melt index time series; the presence of non-integer fractal correlation dimension and positive finite maximum Lyapunov exponent are found in some IMF components. The PP melt index series are divided into two chaotic signals, a determined signal and a random signal respectively, and its complexity is therefore reduced. Furthermore, the coupling of subscale structures of the propylene polymerization is explored with the dimension of interaction dynamics and a robust algorithm for detecting interdependence. It is found that IMF(2) is the main driver in the coupling system of IMF(1)and IMF(2). All these provide a guideline for studying propylene polymerization process with chaotic multiscale theory and may offer more candidate tools to model and control propylene polymerization system in the future.

Compressive consolidation of strongly aggregated particle gels

The compressive yield stress of particle gels shows a highly nonlinear dependence on the packing fraction. We have studied continuous compression processes, and discussed the packing fraction dependence with the particle scale rearrangements. The 2D simulation of uniaxial compression was applied to fractal networks, and the required compressive stresses were evaluated for a wide range of packing fractions that approached close packing. The compression acts to reduce the size of the characteristic structural entities (i.e. the correlation length of the structure). We observed three stages of compression: (I) elastic-dominant regime; (II) single-mode plastic regime, where the network strengths are determined by the typical length scale and the rolling mode; and (III) multi-mode plastic regime, where sliding mode and connection breaks are important. We also investigated the way of losing the fractal correlation under compression. It turns out that both fractal dimension $D_{\mathrm{f}}$ and correlation length $\xi$ start to change from the early stage of compression, which is different from the usual assumption in theoretical models.

Reservoir parameter classification of a Miocene formation using a fractal approach to well logging, porosimetry and nuclear magnetic resonance

A methodology for rock classification is presented that considers lithology and reservoir parameters on the basis of a combined fractal analysis of well logs and mercury porosimetry results with nuclear magnetic resonance outcomes. A sandy-shaly thinly-bedded Miocene gas bearing formation in the Carpathian Foredeep is investigated. Fractal correlation dimensions D2 calculated for standard logs are used to distinguish sandstone as the most homogeneous lithological group with the highest porosity. The fractal analysis also confirmed observations of gas accumulations in sandstone, shaly sandstone and sandy claystone as rocks of high porosity. The results of two laboratory methods are combined to improve reservoir properties assessment and evaluate movable media in pore space; this technique was based on the similarity of mercury porosimetry results plotted as cumulative intrusion volume versus pressure or pore diameter and also the curves of cumulative porosity and transverse relaxation time distributions using nuclear magnetic resonance. Close values of porosity from logs, recorded in situ and in laboratory measurements, provide the link between fractal analysis and porosimetry and nuclear magnetic resonance measurements.

Fractal Correlation Analysis of X-ray Diffraction Patterns with Broad Background

X-ray diffraction (XRD) patterns with broad background are commonly found in powders where crystallization is incomplete or mixed with amorphous material. This is the case of alumina used for, for ...

Detrended fluctuation analysis of blood pressure in preterm infants with intraventricular hemorrhage

Very preterm infants are at high risk of death and serious permanent brain damage, as occurs with intraventricular hemorrhage (IVH). Detrended fluctuation analysis (DFA) that quantifies the fractal correlation properties of physiological signals has been proposed as a potential method for clinical risk assessment. This study examined whether DFA of the arterial blood pressure (ABP) signal could derive markers for the identification of preterm infants who developed IVH. ABP data were recorded from a prospective cohort of 30 critically ill preterm infants in the first 1-3 h of life, 10 of which developed IVH. DFA was performed on the beat-to-beat sequences of mean arterial pressure (MAP), systolic blood pressure (SBP) and pulse interval, with short-term exponent (α1, for timescale of 4-15 beats) and long-term exponent (α2, for timescale of 15-50 beats) computed accordingly. The IVH infants were found to have higher short-term scaling exponents of both MAP and SBP (α1 = 1.06 ± 0.18 and 0.98 ± 0.20) compared to the non-IVH infants (α1 = 0.84 ± 0.25 and 0.78 ± 0.25, P = 0.017 and 0.038, respectively). The results have demonstrated that fractal dynamics embedded in the arterial pressure waveform could provide useful information that facilitates early identification of IVH in preterm infants.

Evolutions of speckles on rough glass/silver surfaces with film thickness

This paper reports experimental studies on speckles produced by the rough silver films. The speckles on the rough glass/silver surfaces are measured with a microscopic imaging system. The structures of speckle patterns have the characteristics of fractals and multi-scaled sizes. We find that with the increase of the silver film thickness, the contrast of the speckles increases, and the intensity probability density functions gradually transit to exponential decay. We calculate the global and the local correlation functions of the speckle patterns, and find that both the fractal exponent and correlation length of the small-sized speckles decrease with the thickness of the silver films. We use the mechanisms of rough dielectric interface scattering and random surface plasmon waves to give the preliminary explanations for the evolutions of the speckles.

Structural transformations in magnetorheological slurries induced by perturbations

The pattern formation produced by the aggregation of the particles in magnetorheological dispersions when they are in the presence of a static magnetic field, and the process of reconstruction of these structures induced by the application of magnetic perturbations, are investigated experimentally and theoretically. Under the influence of a static magnetic field the aggregation of the dispersed particles generates a multifractal structure, whose corresponding hierarchical structure has been characterized by means of its mass fractal dimensions and other correlations. When this system is perturbed by an oscillatory magnetic field, in addition to the static one, the dispersion rearranges becoming, for certain values of the amplitude and frequency of the perturbation, a more compact and relatively more ordered structure. Here, the analysis of these phenomena is approached as if the pattern formation were a kind of glassy transformation in a supercooled liquid, and the effect of the perturbation were an annealing process. The role of the temperature is taken here by the ratio of the intensities of the applied fields. From high resolution photographs taken at different stages of the structure evolution, it is possible to calculate some complexity measures such as the singularity spectrum, the lacunarity index, enthalpy and the configurational entropy. On this basis it is possible to describe quantitatively these glassy-like transformations. The relaxation time that distinguishes between a cooling process that leads the structure to a glassy or a crystalline one, is experimentally obtained.

Multiscale analysis of economic time series by scale-dependent Lyapunov exponent

Economic time series usually exhibit complex behavior such as nonlinearity, fractal long-memory, and non-stationarity. Recently, considerable efforts have been made to detect chaos and fractal long-memory in finance. While evidence supporting fractal scaling in finance has been accumulating, it is now generally thought that financial time series may not be modeled by chaos or noisy chaos, since the estimated Lyapunov exponent (LE) is negative. A negative LE amounts to a negative Kolmogorov entropy, and thus implies simple regular dynamics of the economy. This is at odds with the general observation that the economy is highly complicated due to nonlinear and stochastic interactions among component systems and hierarchical regulations in the world economy. To resolve this dilemma, and to provide an effective means of characterizing fractal long-memory properties in non-stationary economic time series, we employ a multiscale complexity measure, the scale-dependent Lyapunov exponent (SDLE), to characterize economic time series. SDLE cannot only unambiguously distinguish low-dimensional chaos from noise, but also detect high-dimensional and intermittent chaos, as well as effectively deal with non-stationarity. With SDLE, we are able to show that the reported negative LE may correspond to large-scale convergence, but not imply the absence of small-scale divergence or noisy chaos in the world economy. Using US foreign exchange rate data as examples, we further show how SDLE can readily characterize fractal, persistent or anti-persistent long-range correlations in economic time series.

Exploratory Bioinformatics Study of lncRNAs in Alzheimer’s Disease mRNA Sequences with Application to Drug Development

Long noncoding RNA (lncRNA) within mRNA sequences of Alzheimer's disease genes, namely, APP, APOE, PSEN1, and PSEN2, has been analyzed using fractal dimension (FD) computation and correlation analysis. We examined lncRNA by comparing mRNA FD to corresponding coding DNA sequences (CDSs) FD. APP, APOE, and PSEN1 CDSs select slightly higher FDs compared to the mRNA, while PSEN2 CDSs FDs are lower. The correlation coefficient for these sequences is 0.969. A comparative study of differentially expressed MAPK signaling pathway lncRNAs in pancreatic cancer cells shows a correlation of 0.771. Selection of higher FD CDSs could indicate interaction of Alzheimer's gene products APP, APOE, and PSEN1. Including hypocretin sequences (where all CDSs have higher fractal dimensions than mRNA) in the APP, APOE, and PSEN1 sequence analyses improves correlation, but the inclusion of erythropoietin (where all CDSs have higher FD than mRNA) would suppress correlation, suggesting that HCRT, a hypothalamus neurotransmitter related to the wake/sleep cycle, might be better when compared to EPO, a glycoprotein hormone, for targeting Alzheimer's disease drug development. Fractal dimension and entropy correlation have provided supporting evidence, consistent with evolutionary studies, for using a zebrafish model together with a mouse model, in HCRT drug development.

Translational Bioinformatics and Computational Systems Medicine

This special issue is dedicated to Translational bioinformatics and Computational Systems Medicine. Translational biomedical informatics is a rapidly emerging discipline to integrate data from medical research, biotechnologies, and electronic medical records, and computational systems medicine is to apply computational and systems biology approaches to solve complex problems in medical research, aiming to improve the diagnosis, prognosis, and treatment of complex diseases. It is also well known that their development needs an integration of mathematical models, statistical methods, and computer algorithms. Complex diseases such as cancers are coursed by a combination of genetic, environmental, and lifestyle factors, and thus the research of complex diseases at a system level like gene sets, pathway level, or static/dynamic network is a necessity. T. Holden et al. present an exploratory bioinformatics study of long noncoding RNA in Alzheimer's disease. The authors also discuss the model for drug development based on fractal dimension and entropy correlation in this study consistent with a zebrafish model and a mouse model. M. Ding et al. explore the genome-wide chromatin localization of Estrogen receptor-DNA binding regions by analyzing ChIP-Seq data from MCF-7 breast cancer cell line. It reveals novel Estrogen receptor-regulated genes pathways for further experimental validation. Y.-w. Lv et al. perform gene ontology category and pathways analysis for relationships among statistically significant genes in Kawasaki disease. The importance of compelling immune pathway of NF-AT signal and leukocyte interactions combined with another transcription factor NF-κB in the pathogenesis of KD is investigated by network analysis. J. Chen et al. perform two case studies on colorectal and prostate cancer microarray datasets to proof two hypotheses that (1) the expression signatures of different cancer microarray datasets are more similar at pathway level than at gene level; (2) the comparability of the cancer molecular mechanisms of different individuals is related to their genetic similarities. The concept of entropy suggests that systems naturally progress from order to disorder. Entropy-based methods provide a novel insight into understanding many phenomena in biological systems. V. Oswal et al. present an automated entropy-based thresholding system for segmentation and quantification of cell nuclei from histologically stained images. The contributions to the application of this entropy-based system to detect cancerous cell nuclei and observe overlapping cellular events occurring during wound healing process in the human body are also presented. H.-T. Wu et al. investigate the feasibility and sensitivity of a novel multiscale entropy index in detecting subtle vascular abnormalities in healthy and diabetic subjects. The authors further focus on four groups of subjects to discuss the application of multiscale entropy index. The role of protein structures in understanding diseases becomes more and more important, due to the following two reasons. One is that there are a lot of disease-associated proteins that were discovered, while the other fact is that many diseases are believed to result from misfolded proteins. Moreover, protein structures can be considered as complex systems, and thus network theory can be used to characterize and to analyze protein structures. J. Sun et al. present a contribution which focuses on the effect of edge definition of complex networks on protein structure identification. After the performance on 2847 proteins, the authors argue that the optimal cutoff value for constructing the protein structure networks is 5.0 A. X. Jiao et al. improve the amino acid network for proteins by introducing similar weight and dissimilar weight. This work demonstrates that highly central residues of the amino acid network are highly correlated with the hot spots in disease-associated proteins. Finally, two bioinformatics tools were also involved in this issue. H. Wu et al. contribute a bioinformatics tool called patGPCR, to predict the 3D structures of transmembrane helices of G-protein-coupled receptors. patGPCR, a parallelized multitemplate approach, extends a bundle-packing related energy function to RosettaMem energy, which improves the TM RMSD (root mean square deviation of the transmembrane helices) of the predicted models. N. Deng et al. contribute another platform, called crcTRP, for colorectal cancer. This server provides the translational research of colorectal cancer by providing various types of biomedical information, including clinical data, epidemiology data, individual omics data, and public omics data. Bairong Shen Hong-Bin Shen Tianhai Tian Qiang Lu Guang Hu

Effect of Respiration in HRV Analysis using Chaos Theory

This erudite work will scrutinize and then quantify the impacts of respiration in heart-rate variability. Doing so, the critique will be on the basis of fractional mathematics along with chaos theory in two-hundred-and- fifty sick individuals who had heart-failure for the duration of twelve months. In fact, this scholarly work applied a number of non-linear methodologies, encompassing: Approximate-entropy (ApEn), FD (Fractal-dimension, and DFA (detrented fluctuation-analysis). In this scholarly work, fractal dimensions as well as the properties of fractal correlation will be employed in reflecting neuro-anatomic interaction that has been altered, which may prejudice the severe heart failure to start developing. The findings apparently portrayed that the quick-fix fractal scaling- component was appreciably lower in those individuals who had heart failure. Research has found a certain relationship between the breathing with cardiac arrhythmias signal. Moreover, those individuals with heart- failure had a lower approximate-entropy but their fractal- dimension was higher which impacted positively on the new- fangled therapy. 

Accuracy Analysis of Agriculture Soil Surface Roughness Parameter

Agricultural soil surface roughness parameters including surface root mean square height(rms h)and surface correlation length(cl)are key for effectively explaining radar backscattering coefficient and passive microwave brightness temperature,and its measurement accuracy is affected by measured method,measured instruments and data preprocessing.For surface roughness field measurement,the urgent problem is how to evaluate its measurement accuracy.This paper uses two-dimension surface height data from laser scanner and one-dimensional surface height data from Monte Carlo simulation,and analyzes the factors which influence the accuracy of surface roughness including sampling times,sampling interval,profile length,correlation function and large-scale structure(data skew and row structure).Four regions with different surface rough condition are used in this paper for analyzing surface roughness measurement method and accuracy.The result shows that,the measurement accuracy of agriculture soil surface roughness is about 80% under the condition of more than 20 samples,less than 10mm sampling interval and more than 200 cl profile length;the agreement between fractal correlation function and experimental spatial correlation coefficient is higher than Gaussian and exponential correlation function;and the skew and row structure of surface height data seriously affect the result of surface roughness parameter which needs to be removed before surface roughness calculation.

Statistical analysis of petrophysical parameters of Middle Miocene rocks from the Polish Carpathian Foredeep

Normal 0 21 false false false PL X-NONE X-NONE MicrosoftInternetExplorer4 Sarmatian thin-bedded sandy-shaly formation was a subject of statistical studies to differentiate between good and poor reservoir rocks and to show gas-saturated layers in comparison to water-saturated formation. Statistical studies including fractal analysis were performed on well logging data from well S-34 drilled in a belt of hydrocarbon deposits that continued below the northern edge of the Carpathian-Stebnik overthrust. Lithological variability and porosity differentiation and changes in water saturation were traced on the basis of results of well logging interpretation. Basic statistics and histograms of petrophysical parameters were investigated. A generalized fractal correlation dimension of the second order was calculated for all parameters and analyzed in the same way as time series. Fractal dimensions did not correlated with the parameters, but good positive correlations between them and parameters were observed and proved that the analyzed curves had the same type of complexity. High correlation coefficients showed pairs of fractal dimensions for those parameters which had similar variability and the same curve roughness. Fractal correlation dimension described the type of complexity of the parameter (curve roughness) and indicated, for example, how shaliness influenced the reservoir properties of Middle Miocene. Therefore, the results had also the practical side, which gave extra information on thin-bedded reservoir rock formations. Sarmatian thin-bedded sandstone and shales have been a subject of statistical studies to differentiate between good and poor reservoir rocks and to show gas-saturated layers in comparison to water-saturated strata. Statistical studies including fractal analysis were performed on well logging data from the Sędziszów 34 borehole drilled in a belt of hydrocarbon deposits that continue below the northern edge of the Carpathian–Stebnik overthrust. Lithological variability and porosity differentiation and changes in water saturation were traced on the basis of the results of well logging interpretation. Basic statistics and histograms of petrophysical parameters have been analysed. A generalized second order fractal correlation dimension was calculated for all parameters and analysed as for a time series. Fractal dimensions did not correlated with the parameters, but good positive correlations between them and the parameters were observed and showed that the curves analysed had the same type of complexity. High correlation coefficients showed pairs of fractal dimensions for those parameters which had similar variability and the same curve roughness. The fractal correlation dimension described the type of complexity of the parameter (curve roughness) and indicated, for example, how shaliness influenced the reservoir properties of the local Middle Miocene. Therefore, the results were also useful in practice, which gave extra information on thin-bedded reservoir rocks.  

Polymeric self-assembly changes by surface-modified and in-situ-grown nanoparticles

The morphology of polymeric self-assembled structures can be changed by environmental conditions, including pH, temperature, and various additives such as ions, cosolvents, nanoparticles (NPs), and so on. Studies have focused on the size and shape of NPs to investigate the effect of NP incorporation into polymeric structures. In this study, qualitative NP effect is experimentally investigated in terms of the compatibility of NPs with the self-assembled templates. Hydrophobically/hydrophilically surface-modified gold nanoparticles (AuNP) of 20 nm diameter systematically modify the surfactant number (Ns) of the self-assembled organic templates accordingly, where the driving force is determined by the hydrophilic–lipophilic force balance. AuNPs grown in situ at equlibrium in the template, decrease the Ns, reflecting selective growth of NPs in one of the self-assembly domains. Fractal density (α) and correlation length (ζ) of the self-assembled structures are prominently increased by any type of AuNP incorporation.

Dynamical complexity of human responses: a multivariate data-adaptive framework

Abstract Established complexity measures typically operate at a single scale and thus fail to quantify inherent long-range correlations in real-world data, a key feature of complex systems. The recently introduced multiscale entropy (MSE) method has the ability to detect fractal correlations and has been used successfully to assess the complexity of univariate data. However, multivariate observations are common in many real-world scenarios and a simultaneous analysis of their structural complexity is a prerequisite for the understanding of the underlying signal-generating mechanism. For this purpose, based on the notion of multivariate sample entropy, the standard MSE method is extended to the multivariate case, whereby for rigor, the intrinsic multivariate scales of the input data are generated adaptively via the multivariate empirical mode decomposition (MEMD) algorithm. This allows us to gain better understanding of the complexity of the underlying multivariate real-world process, together with more degrees of freedom and physical interpretation in the analysis. Simulations on both synthetic and real-world biological multivariate data sets support the analysis.

Fractal Fluctuations in Quiet Standing Predict the Use of Mechanical Information for Haptic Perception

Movement science has traditionally understood high-dimensional fluctuations as either antithetical or irrelevant to low-dimensional control. However, fluctuations incident to changeful, sometimes unpredictable stimulation must somehow reshape low-dimensional aspects of control through perception. The movement system's fluctuations may reflect cascade dynamics in which many-sized events interact nonlinearly across many scales. Cascades yield fractal fluctuations, and fractality of fluctuations may provide a window on the interactions across scale supporting perceptual processes. To test these ideas, we asked adult human participants to judge whole or partial length for unseen rods (with and without added masses). The participants' only experience with the objects came from supporting them across their shoulders during quiet standing. First, the degree of fractal temporal correlations in trial-by-trial series of planar Euclidean displacements in center of pressure (COP) significantly improved prediction of subsequent trial-by-trial judgments, above and beyond prediction by traditional predictors of haptic perception and conventional measures of COP variability. Second, comparison with linear surrogate data indicated the presence of nonlinear interactions across scale in these time series. These results demonstrate that high-dimensional fluctuations may serve a crucial role in the cascade dynamics supporting apparently low-dimensional control strategies.

A hybrid model-based fault detection strategy for air handling unit sensors

For the air handling unit (AHU) sensor fault detection, the classical fault detection methods based on statistical residual evaluation are difficult to detect small bias fault especially under noisy conditions. On the other hand, a novel technique using fractal correlation dimension (FCD) algorithm can identify a tiny variation of curve fractal characteristic but needs a period of time. To balance their strengths as well as weaknesses, a hybrid model-based fault detection technique is developed by combining these two methods. The simulated data obtained from the TRNSYS simulation platform are used to validate the hybrid fault detection strategy. And a prediction model using support vector regression (SVR) is developed to obtain the fault-free references. Under a noise ranging from −0.3°C to +0.3°C, the technique is validated to detect six fixed biases of the supply air temperature sensor under three different load conditions. Given a specified threshold, the hybrid technique can identify the large bias faults such as ±0.5°C by statistical residuals and can detect small faults of ±0.2°C by FCD deviations. For the dynamic and nonlinear systems, FCD-based approach is more suitable for fault detection than for fault diagnosis.

Fractal Features of Cracked Backfill Particle Size Distribution

Based on the taking sample by geological drilling, combined with the fractal principle, analysis on the cracked backfill particle size of its fractal features and strength correlation. Even each backfill sand specimen particle size is difference, but calculation data shows that the particle size of each sand specimen has preferable fractal feature, the sand specimen particle size distribution has remarkable fractal structure by the linear fitted results of the sand specimens. The fractal relationship of strength and particle size distribution shows that with the increased of fractal dimension, the strength of backfill is decreased, that is to say there is negative correlation, the main cause is that the higher parameter D of the fractal dimension, the higher fine-grained content and more non-uniform of the particle size distribution, especially for the thinner full tailings, if properly increasing the content of slightly crude particles, the strength of backfill will be certainly improved to some extent.

Heart rate variability and nonlinear dynamic analysis in patients with stress-induced cardiomyopathy

Complexity-based analyses may quantify abnormalities in heart rate variability (HRV). The aim of this study was to investigate the clinical and prognostic significances of dynamic HRV changes in patients with stress-induced cardiomyopathy Takotsubo syndrome (TS) by means of linear and nonlinear analysis. Patients with TS were included in study after complete noninvasive and invasive cardiovascular diagnostic evaluation and compared to an age and gender matched control group of healthy subjects. Series of R-R interval and of ST-T interval values were obtained from 24-h ECG recordings after digital sampling. HRV analysis was performed by 'range rescaled analysis' to determine the Hurst exponent, by detrended fluctuation analysis to quantify fractal long-range correlation properties, and by approximate entropy to assess time-series predictability. Short- and long-term fractal-scaling exponents were significantly higher in patients with TS in acute phases, opposite to lower approximate entropy and Hurst exponent, but all variables normalized in a few weeks. Dynamic HRV analysis allows assessing changes in complexity features of HRV in TS patients during the acute stage, and to monitor recovery after treatment, thus complementing traditional ECG and clinically analysis.