Fractal Scaling Research Articles

Conflicts hurt: Social stress modulates proinflammatory cytokines’ link with pain and sadness

Several parameters of heart rate variability (HRV) have been shown to predict the risk of sudden cardiac death (SCD) in cardiac patients. There is consensus that risk prediction is increased when measuring HRV during specific provocations such as orthostatic challenge. For the first time, we provide data on reproducibility of such a test in patients with a history of acute coronary syndrome.Sixty male patients (65 ± 8 years) with a history of acute coronary syndrome on stable medication were included. HRV was measured in supine (5 min) and standing (5 min) position on 2 occasions separated by two weeks. For risk assessment relevant time-domain [standard deviation of all R-R intervals (SDNN) and root mean squared standard differences between adjacent R-R intervals (RMSSD)], frequency domain [low-frequency power (LF), high-frequency power (HF) and LF/HF power ratio] and short-term fractal scaling component (DF1) were computed. Absolute reproducibility was assessed with the standard errors of the mean (SEM) and 95% limits of random variation, and relative reproducibility by the intraclass correlation coefficient (ICC).We found comparable SEMs and ICCs in supine position and after an orthostatic challenge test. All ICCs were good to excellent (ICCs between 0.636 and 0.869).Reproducibility of HRV parameters during orthostatic challenge is good and comparable with supine position.

Task-dependent fractal patterns of information processing in working memory

We applied detrended fluctuation analysis, power spectral density, and eigenanalysis of detrended cross-correlations to investigate fMRI data representing a diurnal variation of working memory in four visual tasks: two verbal and two nonverbal. We show that the degree of fractal scaling is regionally dependent on the engagement in cognitive tasks. A particularly apparent difference was found between memorisation in verbal and nonverbal tasks. Furthermore, the detrended cross-correlations between brain areas were predominantly indicative of differences between resting state and other tasks, between memorisation and retrieval, and between verbal and nonverbal tasks. The fractal and spectral analyses presented in our study are consistent with previous research related to visuospatial and verbal information processing, working memory (encoding and retrieval), and executive functions, but they were found to be more sensitive than Pearson correlations and showed the potential to obtain other subtler results. We conclude that regionally dependent cognitive task engagement can be distinguished based on the fractal characteristics of BOLD signals and their detrended cross-correlation structure.

Quorum-sensing control of matrix protein production drives fractal wrinkling and interfacial localization of Vibrio cholerae pellicles

Bacterial cells at fluid interfaces can self-assemble into collective communities with stunning macroscopic morphologies. Within these soft, living materials, called pellicles, constituent cells gain group-level survival advantages including increased antibiotic resistance. However, the regulatory and structural components that drive pellicle self-patterning are not well defined. Here, using Vibrio cholerae as our model system, we report that two sets of matrix proteins and a key quorum-sensing regulator jointly orchestrate the sequential mechanical instabilities underlying pellicle morphogenesis, culminating in fractal patterning. A pair of matrix proteins, RbmC and Bap1, maintain pellicle localization at the interface and prevent self-peeling. A single matrix protein, RbmA, drives a morphogenesis program marked by a cascade of ever finer wrinkles with fractal scaling in wavelength. Artificial expression of rbmA restores fractal wrinkling to a ΔrbmA mutant and enables precise tuning of fractal dimensions. The quorum-sensing regulatory small RNAs Qrr1-4 first activate matrix synthesis to launch pellicle primary wrinkling and ridge instabilities. Subsequently, via a distinct mechanism, Qrr1-4 suppress fractal wrinkling to promote fine modulation of pellicle morphology. Our results connect cell-cell signaling and architectural components to morphogenic patterning and suggest that manipulation of quorum-sensing regulators or synthetic control of rbmA expression could underpin strategies to engineer soft biomaterial morphologies on demand.

Characterization of interlayer mechanical performance of double-layer porous asphalt compacted by three methods: Simulations and observations

The compaction method directly governs the interlayer patterns, which significantly influence the performance of asphalt pavement. The objective of this research aimed to investigate the interlayer mechanical performance of double-layer porous asphalt (DLPA) samples compacted by three methods: hot-on-cold (HoC), hot-on-warm (HoW), and hot-on-hot (HoH). The interlayer patterns at the upper-lower layer interface of DLPA samples were measured by the thin aluminum sheet and oil-saturated paper and characterized by the modified Weierstrass-Mandelbrot (W-M) function with two fractal parameters. The virtual direct shear test and pull-off test were conducted on the simulated DLPA samples incorporating interlayer patterns. The interlayer mechanical strengths from simulation were verified by laboratory experiments. The results showed that the fractal dimension and scale parameter in the modified W-M function characterized the interlayer patterns. The DLPA samples using HoH compaction exhibited the highest shear and tensile strengths that were inversely proportional to the fractal dimension, owing to the interlocking interlayer pattern generated. The HoH method was recommended to compact the DLPA pavement if the double-layer asphalt paver was available. The findings are useful to improve construction quality of the DLPA pavement.

Multifractal Characteristics of China’s Stock Market and Slump’s Fractal Prediction

It is necessary to quantitatively describe or illustrate the characteristics of abnormal stock price fluctuations in order to prevent and control financial risks. This paper studies the fractal structure of China’s stock market by calculating the fractal dimension and scaling behavior on the timeline of its eight big slumps, the results show that the slumps have multifractal characteristics, which are correlated with the policy intervention, institutional arrangements, and investors’ rationality. The empirical findings are a perfect match with the anomalous features of the stock prices. The fractal dimensions of the eight stock collapses are between 0.84 and 0.98. The fractal dimension distribution of the slumps is sensitive to market conditions and the active degree of speculative trading. The more mature market conditions and the more risk-averse investors correspond to the higher fractal dimension and the fall which is less deep. Therefore, the fractal characteristics could reflect the evolution characteristics of the stock market and investment philosophy. The parameter set calculated in this paper could be used as an effective tool to foresee the slumps on the horizon.

A New Fractal Permeability Model for Porous Media Based on Rough Capillary Channels

Porous media are assumed as a bunch of curved capillaries of rough pore-solid surface, with capillary size distributions and surface roughness following the fractal scaling laws, for which a permeability model is derived to capture both tortuosity and roughness of the pore space in this work. First, the fractal geometry theory and the regarding methods are used to simulate tortuosity and roughness, and then, the permeability of porous media is linked to pore area fractal dimension, tortuosity fractal dimension, relative mean roughness, and other structural parameters (e.g., characteristic length and maximum and minimum pore size). Each parameter in the proposed model has specific physical meaning, which is able to reveal certain mechanisms that affect permeability comprehensively. For several porous media samples, the predicted permeability data based on the current fractal model are compared with the experimental measurement data and the permeability model predictions for other porous media with smooth capillary channels. A good agreement was found between the predicted values of the new permeability fractal model and the experimental data.

Critical Scaling of Solid Fragmentation at Quasistatic and Finite Strain Rates.

Using two-dimensional simulations of sheared, brittle solids, we characterize the resulting fragmentation and explore its underlying critical nature. Under quasistatic loading, a power-law distribution of fragment masses emerges after fracture which grows with increasing strain. With increasing strain rate, the maximum size of a grain decreases and a shallower distribution is produced. We propose a scaling theory for distributions based on a fractal scaling of the largest mass with system size in the quasistatic limit or with a correlation length that diverges as a power of rate in the finite-rate limit. Critical exponents are measured using finite-size scaling techniques.

A rail corrugation evaluation method using fractal characterization based on structure function method

The long-standing problem of rail corrugation has not yet been effectively solved. The evaluation index for rail corrugation proposed in the existing rail grinding standards generally does not allow the roughness of rail corrugation to be evaluated at multiple scales. And it's not easy to accurately assess the impact of corrugation on the dynamic performance of train operations. Based on the fractal analysis of rail corrugation track irregularity data, this paper proposes several fractal indices suitable for evaluating quantitatively the effect of rail corrugation irregularity on the fluctuations of the wheel-rail force. The research shows that the rail corrugation evaluation index best correlated with the wheel-rail force fluctuation index are corrected fractal dimension and scale coefficient. The coefficient of determination, R-square, of the proposed model is about 0.9, while that of the traditional rail corrugation evaluation index is only 0.7, an increase by 28.5%. An empirical formula of the relationship between the wheel-rail force fluctuation index and fractal index is established, which can guide subway track structural design and rail grinding.

Economic Choice and Heart Rate Fractal Scaling Indicate That Cognitive Effort Is Reduced by Depression and Boosted by Sad Mood

BackgroundPeople with depression typically exhibit diminished cognitive control. Control is subjectively costly, prompting speculation that control deficits reflect reduced cognitive effort. Evidence that people with depression exert less cognitive effort is mixed, however, and motivation may depend on state affect. MethodsWe used a cognitive effort discounting task to measure propensity to expend cognitive effort and fractal structure in the temporal dynamics of interbeat intervals to assess on-task effort exertion for 49 healthy control subjects, 36 people with current depression, and 67 people with remitted depression. ResultsPeople with depression discounted more steeply, indicating that they were less willing to exert cognitive effort than people with remitted depression and never-depressed control subjects. Also, steeper discounting predicted worse functioning in daily life. Surprisingly, a sad mood induction selectively boosted motivation among participants with depression, erasing differences between them and control subjects. During task performance, depressed participants with the lowest cognitive motivation showed blunted autonomic reactivity as a function of load. ConclusionsDiscounting patterns supported the hypothesis that people with current depression would be less willing to exert cognitive effort, and steeper discounting predicted lower global functioning in daily life. Heart rate fractal scaling proved to be a highly sensitive index of cognitive load, and data implied that people with lower motivation for cognitive effort had a diminished physiological capacity to respond to rising cognitive demands. State affect appeared to influence motivation among people with current depression given that they were more willing to exert cognitive effort following a sad mood induction.

Synchronization performance affects gait variability measures during cued walking

BackgroundIncorporating variability within gait rehabilitation offers a promising approach to restore functional capacity. However, it’s success requires adequate synchronization, a parameter that lacks report in most of the literature regarding cued gait training. Research questionHow changes to synchronization performance during fractal-like and isochronous cueing impacts gait variability measures? MethodsWe asked twelve young male participants to walk in synchronization to two different temporally structure cueing (isochronous [ISO] and fractal [FRC]). We have also manipulated the cueing’s tempo by increasing and decreasing it by 5% to manipulate synchronization, resulting in six conditions (stimuli [ISO,FRC] x tempo [SLOW, NORMAL, FAST]). The normal condition was set from an uncued trial through the participant’s self-paced stride time. Synchronization performance (ASYNC) and gait variability (fractal scaling and coefficient of variation) were calculated from stride time data ( -ISIs,CV-ISIs). Repeated measures analysis of variance or Aligned Rank Transform were conducted to determine significant differences between metronome tempo and stimuli for the dependent variables ResultsOur results showed a FAST tempo decreases synchronization performance (ASYNC) and leads to lower -ISIs, for both ISO and FRC stimuli. This indicates that when an individual exhibits poor synchronization during cued gait training, his/her gait variability patterns will not follow the temporal structure of the presented metronome. Specifically, if the individual poorly synchronizes to the cues, the gait patterns become more random, a condition typically observed in older adults and neurological patients, which runs contrary to the hypothesis when using fractal-like metronomes. SignificanceThis study provides supporting evidence that measuring synchronization performance in cued training is fundamental for a proper clinical interpretation of its effects. This is particularly relevant for the recent and ongoing clinical research using fractal-like metronomes since the expected gait patterns are dependent on the synchronization performance. Randomized control trials must incorporate synchronization performance related measures.

Metastability, fractal scaling, and synergistic information processing: What phase relationships reveal about intrinsic brain activity

Dynamic functional connectivity (dFC) in resting-state fMRI holds promise to deliver candidate biomarkers for clinical applications. However, the reliability and interpretability of dFC metrics remain contested. Despite a myriad of methodologies and resulting measures, few studies have combined metrics derived from different conceptualizations of brain functioning within the same analysis - perhaps missing an opportunity for improved interpretability. Using a complexity-science approach, we assessed the reliability and interrelationships of a battery of phase-based dFC metrics including tools originating from dynamical systems, stochastic processes, and information dynamics approaches. Our analysis revealed novel relationships between these metrics, which allowed us to build a predictive model for integrated information using metrics from dynamical systems and information theory. Furthermore, global metastability - a metric reflecting simultaneous tendencies for coupling and decoupling - was found to be the most representative and stable metric in brain parcellations that included cerebellar regions. Additionally, spatiotemporal patterns of phase-locking were found to change in a slow, non-random, continuous manner over time. Taken together, our findings show that the majority of characteristics of resting-state fMRI dynamics reflect an interrelated dynamical and informational complexity profile, which is unique to each acquisition. This finding challenges the interpretation of results from cross-sectional designs for brain neuromarker discovery, suggesting that individual life-trajectories may be more informative than sample means.

Investigating Fractal Analysis as a Diagnostic Tool That Probes the Connectivity of Hippocampal Neurons.

Many of nature’s fractal objects benefit from the favorable functionality that results from their pattern repetition at multiple scales. Our recent research focused on the importance of fractal scaling in establishing connectivity between neurons. Fractal dimension D A of the neuron arbors was shown to relate to the optimization of competing functional constraints—the ability of dendrites to connect to other neurons versus the costs associated with building the dendrites. Here, we consider whether pathological states of neurons might affect this fractal optimization and if changes in D A might therefore be used as a diagnostic tool in parallel with traditional measures like Sholl analyses. We use confocal microscopy to obtain images of CA1 pyramidal neurons in the coronal plane of the dorsal rat hippocampus and construct 3-dimensional models of the dendritic arbors using Neurolucida software. We examine six rodent groups which vary in brain condition (whether they had lesions in the anterior thalamic nuclei, ATN) and experience (their housing environment and experience in a spatial task). Previously, we showed ATN lesions reduced spine density in hippocampal CA1 neurons, whereas enriched housing increased spine density in both ATN lesion and sham rats. Here, we investigate whether ATN lesions and experience also effect the complexity and connectivity of CA1 dendritic arbors. We show that sham rats exposed to enriched housing and spatial memory training exhibited higher complexity (as measured by D A ) and connectivity compared to other groups. When we categorize the rodent groups into those with or without lesions, we find that both categories achieve an optimal balance of connectivity with respect to material cost. However, the D A value used to achieve this optimization does not change between these two categories, suggesting any morphological differences induced by the lesions are too small to influence the optimization process. Accordingly, we highlight considerations associated with applying our technique to publicly accessible repositories of neuron images with a broader range of pathological conditions.

Insulin signaling shapes fractal scaling of C. elegans behavior

Fractal scaling in animal behavioral activity, where similar temporal patterns appear repeatedly over a series of magnifications among time scales, governs the complex behavior of various animal species and, in humans, can be altered by neurodegenerative diseases and aging. However, the mechanism underlying fractal scaling remains unknown. Here, we cultured C. elegans in a microfluidic device for 3 days and analyzed temporal patterns of C. elegans activity by fractal analyses. The residence-time distribution of C. elegans behaviors shared a common feature with those of human and mice. Specifically, the residence-time power-law distribution of the active state changed to an exponential-like decline at a longer time scale, whereas the inactive state followed a power-law distribution. An exponential-like decline appeared with nutrient supply in wild-type animals, whereas this decline disappeared in insulin-signaling-defective daf-2 and daf-16 mutants. The absolute value of the power-law exponent of the inactive state distribution increased with nutrient supply in wild-type animals, whereas the value decreased in daf-2 and daf-16 mutants. We conclude that insulin signaling differentially affects mechanisms that determine the residence time in active and inactive states in C. elegans behavior. In humans, diabetes mellitus, which is caused by defects in insulin signaling, is associated with mood disorders that affect daily behavioral activities. We hypothesize that comorbid behavioral defects in patients with diabetes may be attributed to altered fractal scaling of human behavior.

The impact of COVID-19 on shipping freights: asymmetric multifractality analysis

ABSTRACT In order to study the asymmetric multifractality in maritime shipping freight rates, we have resorted to the use of the novel approach of asymmetric Multifractality Detrended Fluctuation Analysis. This approach examines the maritime shipping freight response towards the downward and upward movements. The outcomes in this regard show that the major maritime shipping freight rates have multifractals, which tend to increase as the fractal scale also increases. Also, a higher level of multifractality is observed in the downward movements for the Baltic Dry Index, and the Baltic Clean Tanker Index, suggesting that both the indexes have been less efficient, and also unpredictable during the time period pertaining to the pandemic. Moreover, the multifractality is observed to be greater in the upside for the Baltic Dirty Tanker Index during the pandemic, and also in the full-time period. The results also propagate that the maritime shipping freight rates are inefficient, a situation that has been evidently visible during the time period pertaining to the COVID-19 pandemic. The maritime shipping freight rates require special attention to monitor such sudden changes in the price dynamics, and following strict regulations is extremely critical in this regard.

Pulsed laser deposition of carbon nanofoam

We present a comprehensive study about the fabrication of porous, fractal-like nanostructured carbon materials, known as carbon nanofoam, through the Pulsed Laser Deposition (PLD) technique with nanosecond (ns-PLD) and femtosecond (fs-PLD) laser pulses ablating a pyrolitic graphite target. Carbon nanofoams have attracted considerable interest for applications of great societal and technological relevance. Among different fabrication methods, PLD emerged as a versatile tool that allows the depositon of nanostructured films on virtually any kind of substrate. Here we investigate the role of key PLD parameters (laser pulse duration and fluence, background gas pressure) on nanofoam characteristics, with a specific focus on how fractal aggregate properties at the nanometric scale (nanoparticle size, fractal dimension, gyration radius) determine nanofoam averaged properties such as density and uniformity. We performed systematic deposition campaigns and characterizations through experimental analysis and mathematical models. Moreover, a first-of-its-kind comparison between ns-PLD and fs-PLD regimes is drawn. We discuss the physics of foam growth in both regimes, and we propose an analytical model based on the fractal scaling law to predict the nanofoam density from aggregates’ properties. The new insights gained about deposition and characterization of carbon nanofoam open new perspectives in fabrication of nanostructured films with precisely controlled properties.

Fractal Sentiments and Fairy Tales - Fractal scaling of narrative arcs as predictor of the perceived quality of Andersen's fairy tales

This article explores the sentiment dynamics present in narratives and their contribution to literary appreciation. Specifically, we investigate whether a certain type of sentiment development in a literary narrative correlates with its quality as perceived by a large number of readers. While we do not expect a story's sentiment arc to relate directly to readers' appreciation, we focus on its internal coherence as measured by its sentiment arc's level of fractality as a potential predictor of literary quality. To measure the arcs' fractality we use the Hurst exponent, a popular measure of fractal patterns that reflects the predictability or self-similarity of a time series. We apply this measure to the fairy tales of H.C. Andersen, using GoodReads' scores to approximate their level of appreciation. Based on our results we suggest that there might be an optimal balance between predictability and surprise in a sentiment arcs' structure that contributes to the perceived quality of a narrative text.

A Single Subject, Feasibility Study of Using a Non-Contact Measurement to "Visualize" Temperature at Body-Seat Interface.

Measuring temperature changes at the body-seat interface has been drawing increased attention from both industrial and scientific fields, due to the increasingly sedentary nature from daily leisure activity to routine work. Although contact measurement is considered the gold standard, it can affect the local micro-environment and the perception of sitting comfort. A non-contact temperature measurement system was developed to determine the interface temperature using data gathered unobtrusively and continuously from an infrared sensor (IRs). System performance was evaluated regarding linearity, hysteresis, reliability and accuracy. Then a healthy participant sat for an hour on low/intermediate density foams with thickness varying from 0.5–8 cm while body-seat interface temperature was measured simultaneously using a temperature sensor (contact) and an IRs (non-contact). IRs data were filtered with empirical mode decomposition and fractal scaling indices before a data-driven artificial neural network was utilized to estimate the contact surface temperature. A strong correlation existed between non-contact and contact temperature measurement ( > 0.85) and the estimation results showed a low root mean square error (RMSE) (<0.07 for low density foam and <0.16 for intermediate density foam) and high Nash-Sutcliff efficiency (NSE) values (≈1 for both types of foam materials).

Fractal Dimension Analysis of Earth Magnetic Field during 26 August 2018 Geomagnetic Storm

We analyse the fractal nature of geomagnetic field northward and eastward horizontal components with 1 min resolution measured by the four stations Belsk, Hel, Sodankylä and Hornsund during the period of 22 August–1 September, when the 26 August 2018 geomagnetic storm appeared. To reveal and to quantitatively describe the fractal scaling of the considered data, three selected methods, structure function scaling, Higuchi, and detrended fluctuation analysis are applied. The obtained results show temporal variation of the fractal dimension of geomagnetic field components, revealing differences between their irregularity (complexity). The values of fractal dimension seem to be sensitive to the physical conditions connected with the interplanetary shock, the coronal mass ejection, the corotating interaction region, and the high-speed stream passage during the storm development. Especially, just after interplanetary shock occurrence, a decrease in the fractal dimension for all stations is observed, not straightforwardly visible in the geomagnetic field components data.

Multifractal dimensions of soil particle size distribution reveal the erodibility and fertility of alpine grassland soils in the Northern Tibet Plateau

Climate change and human activities have seriously degraded alpine grassland, potentially affecting soil particle size distribution (PSD) and further influencing the nutrient levels and erodibility of soil. Predicting the fertility and erodibility of alpine soil using multifractal dimensions of soil PSD could be used to enhance the management and restoration of degraded alpine grasslands. In the present study, we evaluated three types of alpine grasslands: alpine meadow (AM), alpine steppe (AS), and alpine desert steppe (ADS). Fencing and grazing management measures were conducted at sites containing each grassland type. Then, we analyzed the PSDs, erodibility, and other properties of soil in the 0–20 cm soil layer. Multifractal characterization of soil PSD was calculated using the fractal scale theory. The findings showed that grassland type significantly impacted soil nutrients and the multifractal dimensions of soil PSDs, whereas management measures affected soil erodibility significantly. The proportion of finer particles decreased as follows: AM > AS > ADS. Compared to grazing, fencing enhanced clay content and reduced the proportion of coarser particles under all three grassland types. AM had higher organic carbon and nitrogen levels than AS and ADS. Multifractal dimensions were highest for AM, with ADS having higher erodibility than AM and AS. Multifractal dimensions (except for correlation dimension) also had significantly positive relationships with soil organic carbon and available nutrient content and soil erodibility, but had significantly negative correlations with soil pH, bulk density, and electrical conductivity. Thus, the multifractal dimensions of soil PSDs could be used to characterize the erodibility and fertility characteristics of soil in alpine regions, providing a reference for assessing vegetation restoration measures in the Northern Tibet Plateau.

COMPLEX NETWORKS MODELED ON A KIND OF SIERPIŃSKI-LIKE CARPET

In this paper, we use a kind of Sierpiński-like carpet to construct a special evolving network, whose nodes are all the solid squares in the construction of the carpet up to stage t. In our network, two nodes are neighbors if and only if the intersection of their corresponding squares is a line segment. Using the encoding method in fractal geometry, we show that our evolving network is scale-free and has the small-world effect, but is not fractal scaling.