Fractal Dynamics Research Articles

MOBBING SYNDROME: MENTAL ECOLOGY OF DESTRUCTIVE PROFESSIOGENESIS

Mobbing has entered reference books as the syndrome including harassment and insult of employees in the workplaces for the purpose of constraint for dismissal. In the framework of the synergetic methodology, fractal dynamics of mobbing sociogenesis, psychogenesis and somatogenesis have been separated. Approaches to early diagnostics and prevention in the framework of the strategies of adaptive professiogenesis formation have been explained. A system approach to development of preventive-correctional and treatment-rehabilitation medico-psychosocial programs has been proposed.

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.

Reduced heart rate variability during sleep in long-duration spaceflight

Limited data are available to describe the regulation of heart rate (HR) during sleep in spaceflight. Sleep provides a stable supine baseline during preflight Earth recordings for comparison of heart rate variability (HRV) over a wide range of frequencies using both linear, complexity, and fractal indicators. The current study investigated the effect of long-duration spaceflight on HR and HRV during sleep in seven astronauts aboard the International Space Station up to 6 mo. Measurements included electrocardiographic waveforms from Holter monitors and simultaneous movement records from accelerometers before, during, and after the flights. HR was unchanged inflight and elevated postflight [59.6 ± 8.9 beats per minute (bpm) compared with preflight 53.3 ± 7.3 bpm; P < 0.01]. Compared with preflight data, HRV indicators from both time domain and power spectral analysis methods were diminished inflight from ultralow to high frequencies and partially recovered to preflight levels after landing. During inflight and at postflight, complexity and fractal properties of HR were not different from preflight properties. Slow fluctuations (<0.04 Hz) in HR presented moderate correlations with movements during sleep, partially accounting for the reduction in HRV. In summary, substantial reduction in HRV was observed with linear, but not with complexity and fractal, methods of analysis. These results suggest that periodic elements that influence regulation of HR through reflex mechanisms are altered during sleep in spaceflight but that underlying system complexity and fractal dynamics were not altered.

Statistical persistence and timing characteristics of repetitive circle drawing in children with ASD

Objective: Standardized tests to assess movement difficulties in autism spectrum disorder (ASD) evaluate motor output, but do not provide information about underlying dynamics. The objective of this research is to study the statistical persistence and temporal dynamics of a circle drawing task in children with ASD.Methods: For this study 15 children diagnosed with ASD, aged 4–8 years, were asked to draw circles under various conditions using a computerized tablet. We then assessed fractal dynamics and global temporal dynamics (mean and coefficient of variation) and compared these quantities to those of typically developing (TD) controls.Results: No difference in statistical persistence was found between children with ASD and TD children. Temporal measures showed increased variability in the ASD population in the discontinuous task.Conclusion: Results support the hypothesis that children with ASD have an intact ability to consistently produce continuous movements, but increased variability in production of discontinuous movements.

Effects of autonomic ganglion blockade on fractal and spectral components of blood pressure and heart rate variability in free-moving rats

Fractal analysis is a promising tool for assessing autonomic influences on heart rate (HR) and blood pressure (BP) variability. The temporal spectrum of scale coefficients, α(t), was recently proposed to describe the cardiovascular fractal dynamics. Aim of our work is to evaluate sympathetic influences on cardiovascular variability analyzing α(t) and spectral powers of HR and BP after ganglionic blockade. BP was recorded in 11 rats before and after autonomic blockade by hexamethonium infusion (HEX). Systolic and diastolic BP, pulse pressure and pulse interval were derived beat-by-beat. Segments longer than 5 min were selected at baseline and HEX to estimate power spectra and α(t). Comparisons were made by paired t-test. HEX reduced all spectral components of systolic and diastolic BP, the reduction being particularly significant around the frequency of Mayer waves; it induced a reduction on α(t) coefficients at t<2s and an increase on coefficients at t>8s. HEX reduced only slower components of pulse interval power spectrum, but decreased significantly faster scale coefficients (t<8s). HEX only marginally affected pulse pressure variability. Results indicate that the sympathetic outflow contributes to BP fractal dynamics with fractional Gaussian noise (α<1) at longer scales and fractional Brownian motion (α>1) at shorter scales. Ganglionic blockade also removes a fractional Brownian motion component at shorter scales from HR dynamics. Results may be explained by the characteristic time constants between sympathetic efferent activity and cardiovascular effectors. Therefore fractal analysis may complete spectral analysis with information on the correlation structure of the data.

Dynamics of semiflexible regular hyperbranched polymers

We study the dynamics of semiflexible Vicsek fractals (SVF) following the framework established by Dolgushev and Blumen [J. Chem. Phys. 131, 044905 (2009)], a scheme which allows to model semiflexible treelike polymers of arbitrary architecture. We show, extending the methods used in the treatment of semiflexible dendrimers by Fürstenberg et al. [J. Chem. Phys. 136, 154904 (2012)], that in this way the Langevin-dynamics of SVF can be treated to a large part analytically. For this we show for arbitrary Vicsek fractals (VF) how to construct complete sets of eigenvectors; these reduce considerably the diagonalization problem of the corresponding equations of motion. In fact, such eigenvector sets arise naturally from a hierarchical procedure which follows the iterative construction of the VF. We use the obtained eigenvalues to calculate the loss moduli G(")(ω) of SVF for different degrees of stiffness of the junctions. Finally, we compare the results for SVF to those found for semiflexible dendrimers.

On relative degree, chattering and fractal nature of parasitic dynamics in sliding mode control

With respect to relative degree and chattering in sliding mode (SM) control systems, the notion of fractal dynamics is introduced, and a conjecture is formulated that the character of parasitic dynamics of real control systems is fractal. A model of fractal dynamics is proposed. The characteristics of fractal dynamics are studied in the frequency and time domains. It is shown that with fractal parasitic dynamics SM control systems will always feature chattering and non-ideal closed-loop performance. An example of analysis is provided.

Non-linear dynamics of human locomotion: effects of rhythmic auditory cueing on local dynamic stability

It has been observed that times series of gait parameters [stride length (SL), stride time (ST), and stride speed (SS)], exhibit long-term persistence and fractal-like properties. Synchronizing steps with rhythmic auditory stimuli modifies the persistent fluctuation pattern to anti-persistence. Another non-linear method estimates the degree of resilience of gait control to small perturbations, i.e., the local dynamic stability (LDS). The method makes use of the maximal Lyapunov exponent, which estimates how fast a non-linear system embedded in a reconstructed state space (attractor) diverges after an infinitesimal perturbation. We propose to use an instrumented treadmill to simultaneously measure basic gait parameters (time series of SL, ST, and SS from which the statistical persistence among consecutive strides can be assessed), and the trajectory of the center of pressure (from which the LDS can be estimated). In 20 healthy participants, the response to rhythmic auditory cueing (RAC) of LDS and of statistical persistence [assessed with detrended fluctuation analysis (DFA)] was compared. By analyzing the divergence curves, we observed that long-term LDS (computed as the reverse of the average logarithmic rate of divergence between the 4th and the 10th strides downstream from nearest neighbors in the reconstructed attractor) was strongly enhanced (relative change +73%). That is likely the indication of a more dampened dynamics. The change in short-term LDS (divergence over one step) was smaller (+3%). DFA results (scaling exponents) confirmed an anti-persistent pattern in ST, SL, and SS. Long-term LDS (but not short-term LDS) and scaling exponents exhibited a significant correlation between them (r = 0.7). Both phenomena probably result from the more conscious/voluntary gait control that is required by RAC. We suggest that LDS and statistical persistence should be used to evaluate the efficiency of cueing therapy in patients with neurological gait disorders.

Can the Chaotic Nature of Parkinson’s Disease Be Used to Evaluate the Effect of Medication on Parkinson's Disease Symptoms?

Back to table of contents Previous article Next article LettersFull AccessCan the Chaotic Nature of Parkinson’s Disease Be Used to Evaluate the Effect of Medication on Parkinson's Disease Symptoms?Aboozar Taherkhani, M.Sc.Aboozar TaherkhaniSearch for more papers by this author, M.Sc.Published Online:1 Jan 2013https://doi.org/10.1176/appi.neuropsych.12010008AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InEmail To the Editor: Parkinson's disease (PD) is the second most common neurodegenerative disorder after Alzheimer’s disease. Patients with PD develop motor symptoms such as muscular rigidity, slowness of movement, and reduced gait speed, as well as non-motor deficits such as disorders of mood and distinctive alteration of speech and voice (hypokinetic dysarthria).1 The severity of PD can be detected by these symptoms.Experimental and theoretical evidence shows that complex biological systems, especially the nervous system, have non-linear and chaotic properties.2 Investigations of chaotic activities in physiologic systems suggest that changes in non-linear dynamic measures may indicate states of pathophysiological dysfunction.3,4 Walking is regulated through a complex motor-control system that produces a complex stride interval time series that is characterized by fractal and multi-fractal properties. On the other hand, studies on PD show that, although the chaotic nature of stride interval time is maintained, its chaotic properties change and more or less approach a stochastic state.5 Observations in computer models of the vocal folds and non-linear dynamic analysis of human voices have established the existence of chaos in human voice production. As noted by many researchers, the non-linearities of the voice source mechanisms (i.e., the non-linear pressure flow relation in the glottis, the non-linear stress/strain curves of vocal fold tissues, and the non-linearities associated with vocal fold collision) make this development unsurprising.3 This evidence suggests that chaos theory and non-linear dynamic methods might potentially be applied to diagnose and classify the motor symptoms as well as non-motor deficits in PD and evaluate the effect of medication.Therefore, motor-symptom data (e.g., ambulatory activity data) or non-motor symptoms data (e.g., voice data) can be used to evaluate the effect of medication on the PD symptoms, based on the chaotic nature of PD. As mentioned, pathological dysfunction, especially PD, alters the chaotic property of biological systems. In chaotic states, each time we record the data, different quantities are achieved. It is worth noting that, at any minute, error or noise in experimental conditions leads to a great change in chaotic system results, because chaotic systems are very sensitive to initial and environmental conditions. Hence, some global features of data related to deterministic chaos are needed to evaluate biological behavior.6 Methods based on non-linear dynamics, including general dimension (Hausdorff dimension, information dimension, correlation dimension, etc.), entropy (Kolmogrov entropy, second-order entropy, etc.), and Lyapunov exponents, enable us to quantitatively describe chaotic behavior.3,4 Non-linear features extracted from signals coming from PD patients can be classified by proper classifiers—such as the ones we used in our previous works7—to evaluate the effect of medication on the PD symptoms. Clinical observations are needed to gather labeled data for PD symptoms, especially PD non-motor symptoms (e.g., voice data) during treatment.Amirkabir University of Technology Faculty of Biomedical Engineering Tehran, IranCorrespondence: A.[email protected]ac.irReferences1 Rusz J, Cmejla R, Ruzickova H, et al.: Quantitative acoustic measurements for characterization of speech and voice disorders in early, untreated Parkinson’s disease. J Acoust Soc Am 2011; 129:350–367Crossref, Medline, Google Scholar2 Taherkhani A, Seyyedsalehi SA, Homayoun Jafari A: Design of a chaotic neural network for training and retrieval of grayscale and binary patterns. Neurocomputing 2011; 74(17):2824–2833Crossref, Google Scholar3 Jiang JJ, Zhang Y, McGilligan C: Chaos in voice, from modeling to measurement. Journal of Voice, 03/01/2006Google Scholar4 Taherkhani A, Seyyedsalehi SA, Mohammadi A: Nonlinear Signal Processing for Voice Disorder Detection by Using Modified GP Algorithm and Surrogate Data Analysis. The 7th IEEE International Symposium on Signal Processing and Information Technology 2007, Cairo, EgyptGoogle Scholar5 Goldberger AL, Amaral LA, Hausdorff JM, et al.: Fractal dynamics in physiology: alterations with disease and aging. Proc Natl Acad Sci U S A 2002; 99(Suppl 1):2466–2472Crossref, Medline, Google Scholar6 Sarbaz Y, Towhidkhah F, Gharibzadeh S: Is the chaotic nature of Parkinson’s disease prone to simulation?” J Neuropsychiatry Clin Neurosci 2009; 21:101–102Google Scholar7 Taherkhani A, Seyyedsalehi SA, Mohammadi A: Design of chaotic neural network for robust phoneme recognition. The 8th IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2008, Sarajevo, Bosnia and HerzegovinaGoogle Scholar FiguresReferencesCited byDetailsCited ByNone Volume 25Issue 1 Winter 2013Pages E16-E16 Metrics PDF download History Published online 1 January 2013 Published in print 1 January 2013

Quantifying Fractal Dynamics of Metallogenic Systems with Detrended Fluctuation Analysis

In this paper, we analysed fractional dynamics behavior in metallogenic elements grade series, using detrended fluctuation analysis (DFA), with the objective to explore and understand the underlying dynamic mechanism. Our results show that the metallogenic elements grade series are the scale invariance and the long-range correlation. As in the case of element grade dynamics, the DFA scaling exponents can be used to discriminate mineral intensity.

Fractal Dynamics in a Single Crystal of a Relaxor Ferroelectric

We report the high-resolution and broadband light-scattering spectroscopy of a single crystal of a prototypical relaxor ferroelectric, Pb(Mg(1/3)Nb(2/3))O(3). A self-similar broad central peak, whose intensity is expressed as I(ω) [Symbol: see text] ω(α) has been observed, indicating the presence of a fractal in the crystal. A strong correspondence exists between the temperature dependence of the exponent α and that of the reported behaviors of polar nanoregions. The estimated fractal dimension (d(f) ≈ 2.6) at low temperatures clearly indicates a percolation transition of the polar nanoregions at around 240 K.

Complexity and multifractality of neuronal noise in mouse and human hippocampal epileptiform dynamics

Fractal methods offer an invaluable means of investigating turbulent nonlinearity in non-stationary biomedical recordings from the brain. Here, we investigate properties of complexity (i.e. the correlation dimension, maximum Lyapunov exponent, 1/fγ noise and approximate entropy) and multifractality in background neuronal noise-like activity underlying epileptiform transitions recorded at the intracellular and local network scales from two in vitro models: the whole-intact mouse hippocampus and lesional human hippocampal slices. Our results show evidence for reduced dynamical complexity and multifractal signal features following transition to the ictal epileptiform state. These findings suggest that pathological breakdown in multifractal complexity coincides with loss of signal variability or heterogeneity, consistent with an unhealthy ictal state that is far from the equilibrium of turbulent yet healthy fractal dynamics in the brain. Thus, it appears that background noise-like activity successfully captures complex and multifractal signal features that may, at least in part, be used to classify and identify brain state transitions in the healthy and epileptic brain, offering potential promise for therapeutic neuromodulatory strategies for afflicted patients suffering from epilepsy and other related neurological disorders.

Spatial-temporal dynamics of events in deterministic models of the BTV type

The latticed models of the BTV type with the arbitrary arrangement of cell of underrun of energy are considered, including possibility of additional dissipation in slow time. Qualitative similarity of model events and real seismicity in the following relations is set: fractal dynamics of migration activity, loglinear relationship of maximum of temporal components with magnitude, gathering of events of low grade to the place of future strong ones.

A partisan effect in the efficiency of the US stock market

This work examines the presence of a partisan effect in the US markets over different presidential periods. The analysis is based on the computation of the fractal scaling dynamics of the Dow Jones Industrial Average by means of the detrended fluctuation analysis. The results indicated the presence of several cycles with dominant periods ranging from a 4 to 12 years/cycle. It is argued that these periods are within the range for business cycles reported in the recent literature. On the other hand, it is found that over Democratic terms the stock market tends to deviate from de random walk behavior, which suggests important differences in the economic policies implemented by each political party.

Erratum: Multifractal patterns in the daily catch time series of smooth pink shrimp (Pandalus jordani) from the west coast of Vancouver Island, Canada

There is an urgent need for indicators that anticipate changes in populations of exploited marine species. We modelled the complex patterns of variability found in fisheries time series that are not detected using classical models. We applied fractal analyses to detect time-invariant scaling symmetries in daily catch time series from the smooth pink shrimp (Pandalus jordani) fishery from the west coast of Vancouver Island, British Columbia, Canada. A universal multifractal model, which accounts for intermittent fluctuations and extreme values in a time series, provided a better fit to daily catches than a monofractal model. Multifractality is an indication of multiple scaling patterns and suggests that more than one process is affecting the variability of catches. Fractal dynamics in catch time series were found for a range of scales between 16 and 120 fishing days. To our knowledge, this is the first time that multifractality has been demonstrated for an invertebrate fishery. The multifractal model has t...

Complex and Inverse Complex Dynamics of Fractals using Ishikawa Iteration

Complex graphics of dynamical system have been a subject of intense research nowadays. The fractal geometry is the base of these beautiful graphical images. Many researchers and authors have worked to study the complex nature of the two most popular sets in fractal geometry, the Julia set and the Mandelbrot set, and proposed their work in various forms using existing tools and techniques. Still researches are being conducted to study and reveal the new concepts unexplored in the complexities of these two most popular sets of fractal geometry. Recently, Ashish Negi, Rajeshri Rana and Yashwant S. Chauhan are among those researchers who have contributed a lot in the area of Fractal Geometry applications. In this paper we review the recently done work on complex and inverse complex functions for producing beautiful fractal graphics. The reviewed work mainly emphasizes on the study of the nature of complex and inverse complex functional dynamics using Ishikawa iterates and existence of relative superior Mandel-bar set.

Multifractal patterns in the daily catch time series of smooth pink shrimp (Pandalus jordani) from the west coast of Vancouver Island, Canada

There is an urgent need for indicators that anticipate changes in populations of exploited marine species. We modelled the complex patterns of variability found in fisheries time series that are not detected using classical models. We applied fractal analyses to detect time-invariant scaling symmetries in daily catch time series from the smooth pink shrimp ( Pandalus jordani ) fishery from the west coast of Vancouver Island, British Columbia, Canada. A universal multifractal model, which accounts for intermittent fluctuations and extreme values in a time series, provided a better fit to daily catches than a monofractal model. Multifractality is an indication of multiple scaling patterns and suggests that more than one process is affecting the variability of catches. Fractal dynamics in catch time series were found for a range of scales between 16 and 120 fishing days. To our knowledge, this is the first time that multifractality has been demonstrated for an invertebrate fishery. The multifractal model has the potential to provide an in-season estimate (up to 120 fishing days) of the variability of shrimp catches based on the variability at time scales less than 1 month. Changes in these fractal patterns may provide an early warning that conditions underlying this fishery are changing.

Nonlinear fractal dynamics of human colonic pressure activity based upon the box-counting method

The computational fractal dimension of human colonic pressure activity acquired by a telemetric capsule robot under normal physiological conditions was studied using the box-counting method. The fractal dimension is a numeric value that quantifies to measure how rough the signal is from nonlinear dynamics, rather than its amplitude or other linear statistical features. The colonic pressure activities from the healthy subject during three typical periods were analysed. The results showed that the activity might be fractal with a non-integer fractal dimension after it being integrated over time using the cumsum method, which was never revealed before. Moreover, the activity (after it being integrated) acquired soon after wakening up was the roughest (also the most complex one) with the largest fractal dimension, closely followed by that acquired during sleep with that acquired long time after awakening up (in the daytime) ranking third with the smallest fractal dimension. Fractal estimation might provide a new method to learn the nonlinear dynamics of human gastrointestinal pressure recordings.

Fractal-Driven Distortion of Resting State Functional Networks in fMRI: A Simulation Study

Fractals are self-similar and scale-invariant patterns found ubiquitously in nature. A lot of evidences implying fractal properties such as 1/f power spectrums have been also observed in resting state fMRI time series. To explain the fractal behavior in rs-fMRI, we have proposed the fractal-based model of resting state hemodynamic response function (rs-HRF) whose properties can be summarized by a fractal exponent. Here we show, through a simulation studies, that the fractal behavior of cerebral hemodynamics may cause significant distortion of network properties between neuronal activities and BOLD signals. We simulated neuronal population activities based on the stochastic neural field model from the Macaque brain network, and then obtained their corresponding BOLD signals by convolving them with the rs-HRF filter. The precision of centrality estimated in each node was deteriorated overall in three networks based on transfer entropy, mutual information, and Pearson correlation; particularly the distortion of transfer entropy was more sensitive to the standard deviation of fractal exponents. A node with high centrality was resilient to desynchronized fractal dynamics over all frequencies while a node with small centrality exhibited huge distortion of both wavelet correlation and centrality over low frequencies. This theoretical expectation indicates that the difference of fractal exponents between brain regions leads to discrepancy of statistical network properties, especially at nodes with small centrality, between neuronal activities and BOLD signals, and that the traditional definitions of resting state functional connectivity may not effectively reflect the dynamics of spontaneous neuronal activities.

Fractal dynamics of geomagnetic storms

We explore fluctuations of the horizontal component of the Earth’s magnetic field to identify scaling behaviour of the temporal variability in geomagnetic data recorded by the Intermagnet observatories during the solar cycle 23 (years 1996 to 2005). In this work, we use the remarkable ability of scaling wavelet exponents to highlight the singularities associated with discontinuities present in the magnetograms obtained at two magnetic observatories for six intense magnetic storms, including the sudden storm commencements of 14 July 2000, 29–31 October and 20–21 November 2003. In the active intervals that occurred during geomagnetic storms, we observe a rapid and unidirectional change in the spectral scaling exponent at the time of storm onset. The corresponding fractal features suggest that the dynamics of the whole time series is similar to that of a fractional Brownian motion. Our findings point to an evident relatively sudden change related to the emergence of persistency of the fractal power exponent fluctuations precedes an intense magnetic storm. These first results could be useful in the framework of extreme events prediction studies.