Fractal rigidity in migraine

Łątka, Mirosław; Glaubic-Łatka, Marta; Łątka, Dariusz; West, Bruce J.

doi:10.1016/s0960-0779(03)00440-5

Cited by 16 publications

(12 citation statements)

References 25 publications

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“…Detrended Fluctuations Analysis (see (28) and references therein) is commonly used to determine scaling properties of physiological time series. Its main drawback is associated with strong susceptibility to periodic trends.…”

Section: Determination Of Scaling Propertiesmentioning

confidence: 99%

Fluctuations in Cerebral Hemodynamics

Łątka¹,

Łątka²

2003

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Section: Determination Of Scaling Propertiesmentioning

confidence: 99%

Fluctuations in Cerebral Hemodynamics

Łątka¹,

Łątka²

2003

Self Cite

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“…When dealing with real data, self-similarity is not exact but has a statistical sense, and lower and upper cut-offs necessarily appear. Without the scaling range, the scaling properties may be distinctly different from those of Equations 3 and 4 (Latka et al, 2004; Buiatti et al, 2007). …”

Section: Characteristic Time(s)mentioning

confidence: 97%

Time scales in cognitive neuroscience

Papo¹

2013

Front. Physiol.

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Cognitive neuroscience boils down to describing the ways in which cognitive function results from brain activity. In turn, brain activity shows complex fluctuations, with structure at many spatio-temporal scales. Exactly how cognitive function inherits the physical dimensions of neural activity, though, is highly non-trivial, and so are generally the corresponding dimensions of cognitive phenomena. As for any physical phenomenon, when studying cognitive function, the first conceptual step should be that of establishing its dimensions. Here, we provide a systematic presentation of the temporal aspects of task-related brain activity, from the smallest scale of the brain imaging technique's resolution, to the observation time of a given experiment, through the characteristic time scales of the process under study. We first review some standard assumptions on the temporal scales of cognitive function. In spite of their general use, these assumptions hold true to a high degree of approximation for many cognitive (viz. fast perceptual) processes, but have their limitations for other ones (e.g., thinking or reasoning). We define in a rigorous way the temporal quantifiers of cognition at all scales, and illustrate how they qualitatively vary as a function of the properties of the cognitive process under study. We propose that each phenomenon should be approached with its own set of theoretical, methodological and analytical tools. In particular, we show that when treating cognitive processes such as thinking or reasoning, complex properties of ongoing brain activity, which can be drastically simplified when considering fast (e.g., perceptual) processes, start playing a major role, and not only characterize the temporal properties of task-related brain activity, but also determine the conditions for proper observation of the phenomena. Finally, some implications on the design of experiments, data analyses, and the choice of recording parameters are discussed.

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“…For example, this measure was the most accurate predictor of all-cause mortality in a cohort of 446 survivors of acute myocardial infarction [6]. The "two exponent" approach was used to quantify heart rate variability in various physiological conditions [7][8][9][10][11], dynamics of arterial blood pressure [12,13] and cerebral blood flow [14]. This prompts the question: Is DFA applicable in the short-time limit?…”

Section: Copyright C Epla 2010mentioning

confidence: 99%

Detrended fluctuation analysis of scaling crossover effects

Ignaccolo

Łątka

West

2010

EPL

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Detrended fluctuation analysis (DFA) is one of the most frequently used fractal time series algorithms. DFA has also become the tool of choice for analysis of the short-time fluctuations despite the fact that its validity in this domain has never been demonstrated. We adopt an Ornstein-Uhlenbeck Langevin equation to generate a time series which exhibits short-time powerlaw scaling and incorporates the fundamental property of physiological control systems -negative feedback. To determine the scaling exponent, we derive the analytical expressions for the standard deviation of the solution X(t) of this equation using both the ensemble of statistically independent trajectories and the ensemble obtained by partitioning a single trajectory. The latter approach is used in DFA and many other physiological applications. Surprisingly, the formulas for the standard deviations are different for these two ensembles. We demonstrate that the partitioning amounts to building up deterministic trends that satisfy the "trend + signal" decomposition assumption which is characteristic of DFA. Consequently, the dependence of the rms of DFA residuals F (τ ) on the length τ of data window is the same for both ensembles. The growth of F (τ ) is significantly different from that of the standard deviation of X(t). While the DFA estimate of the shorttime scaling exponent is correct, the polynomial detrending delays the approach of F (τ ) to the asymptotic value by as much as an order of magnitude. This delay may underlie the gradual change of the DFA scaling index typically observed in time series that exhibit crossover between the short-and long-time scaling.

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Fractal rigidity in migraine

Cited by 16 publications

References 25 publications

Fluctuations in Cerebral Hemodynamics

Fluctuations in Cerebral Hemodynamics

Time scales in cognitive neuroscience

Detrended fluctuation analysis of scaling crossover effects

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