Bayesian estimation of self-similarity exponent

Makarava, N.; Benmehdi, Sabah; Holschneider, Matthias

doi:10.1103/physreve.84.021109

Cited by 29 publications

(33 citation statements)

References 100 publications

(137 reference statements)

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“…A signal with scale-invariant correlations does not necessarily imply it possesses fractal patterns in other statistical properties such as multifractality and nonlinearity [15,43]. In addition, there are many other methods for the assessment of correlations that have comparable or even better performances than that of DFA [44]. Further studies using different analytical tools should be encouraged to confirm the observed influence of shift work on multiscale motor activity control.…”

Section: Techniquementioning

confidence: 99%

Simulated shift work in rats perturbs multiscale regulation of locomotor activity

Hsieh

Escobar

Yugay

et al. 2014

J. R. Soc. Interface.

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Motor activity possesses a multiscale regulation that is characterized by fractal activity fluctuations with similar structure across a wide range of timescales spanning minutes to hours. Fractal activity patterns are disturbed in animals after ablating the master circadian pacemaker (suprachiasmatic nucleus, SCN) and in humans with SCN dysfunction as occurs with aging and in dementia, suggesting the crucial role of the circadian system in the multiscale activity regulation. We hypothesized that the normal synchronization between behavioural cycles and the SCN-generated circadian rhythms is required for multiscale activity regulation. To test the hypothesis, we studied activity fluctuations of rats in a simulated shift work protocol that was designed to force animals to be active during the habitual resting phase of the circadian/daily cycle. We found that these animals had gradually decreased mean activity level and reduced 24-h activity rhythm amplitude, indicating disturbed circadian and behavioural cycles. Moreover, these animals had disrupted fractal activity patterns as characterized by more random activity fluctuations at multiple timescales from 4 to 12 h. Intriguingly, these activity disturbances exacerbated when the shift work schedule lasted longer and persisted even in the normal days (without forced activity) following the shift work. The disrupted circadian and fractal patterns resemble those of SCN-lesioned animals and of human patients with dementia, suggesting a detrimental impact of shift work on multiscale activity regulation.

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Section: Techniquementioning

confidence: 99%

Simulated shift work in rats perturbs multiscale regulation of locomotor activity

Hsieh

Escobar

Yugay

et al. 2014

J. R. Soc. Interface.

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“…We used a sliding window in which we calculated the posterior distribution of the Hurst exponent. The width of the window was 150 data points and was chosen based on the validation test [29]. The corresponding time evolution of the posterior probability for the Hurst exponent of the X coordinate time series is shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…See [28] for general background on mixed effects models and [29,30] for details on the Bayesian estimation of H from the observation of Y. As in this reference, for the analysis of the experimental Dictyostelium discoideum cell track data, we took a scaling invariant Jeffreys-like prior for λ [31] with density π (λ) ∼ λ −1 , a flat, (or diffuse) prior for β with density π (β) 1, as well as a flat prior for H with density π (H ) = χ [0,1] [32].…”

Section: B Fractional Brownian Motionmentioning

confidence: 99%

Quantifying the degree of persistence in random amoeboid motion based on the Hurst exponent of fractional Brownian motion

et al. 2014

Self Cite

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Amoebae explore their environment in a random way, unless external cues like, e.g., nutrients, bias their motion. Even in the absence of cues, however, experimental cell tracks show some degree of persistence. In this paper, we analyzed individual cell tracks in the framework of a linear mixed effects model, where each track is modeled by a fractional Brownian motion, i.e., a Gaussian process exhibiting a long-term correlation structure superposed on a linear trend. The degree of persistence was quantified by the Hurst exponent of fractional Brownian motion. Our analysis of experimental cell tracks of the amoeba Dictyostelium discoideum showed a persistent movement for the majority of tracks. Employing a sliding window approach, we estimated the variations of the Hurst exponent over time, which allowed us to identify points in time, where the correlation structure was distorted ("outliers"). Coarse graining of track data via down-sampling allowed us to identify the dependence of persistence on the spatial scale. While one would expect the (mode of the) Hurst exponent to be constant on different temporal scales due to the self-similarity property of fractional Brownian motion, we observed a trend towards stronger persistence for the down-sampled cell tracks indicating stronger persistence on larger time scales.

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“…Among them we mention range scale estimators [10], maximum likelihood [17], KarhunenLoeve expansion [18], p-variation [19], periodograms [20,21], weigthed functional [22], and linear Bayesian models [23].…”

Section: ] B Denotes Expectation Values Taken Over the Values Of Thementioning

confidence: 99%

Quantum probes for fractional Gaussian processes

Paris¹

2014

Physica A: Statistical Mechanics and its Applications

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We address the characterization of classical fractional random noise via quantum probes. In particular, we focus on estimation and discrimination problems involving the fractal dimension of the trajectories of a system subject to fractional Brownian noise. We assume that the classical degree of freedom exposed to the environmental noise is coupled to a quantum degree of freedom of the same system, e.g. its spin, and exploit quantum limited measurements on the spin part to characterize the classical fractional noise. More generally, our approach may be applied to any two-level system subject to dephasing perturbations described by fractional Brownian noise, in order to assess the precision of quantum limited measurements in the characterization of the external noise. In order to assess the performances of quantum probes we evaluate the Bures metric, as well as the Helstrom and the Chernoff bound, and optimize their values over the interaction time. We find that quantum probes may be successfully employed to obtain a reliable characterization of fractional Gaussian process when the coupling with the environment is weak or strong. In the first case decoherence is not much detrimental and for long interaction times the probe acquires information about the environmental parameters without being too much mixed. Conversely, for strong coupling information is quickly impinged on the quantum probe and can effectively retrieved by measurements performed in the early stage of the evolution. In the intermediate situation, none of the two above effects take place: information is flowing from the environment to the probe too slowly compared to decoherence, and no measurements can be effectively employed to extract it from the quantum probe. The two regimes of weak and strong coupling are defined in terms of a threshold value of the coupling, which itself increases with the fractional dimension.

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Bayesian estimation of self-similarity exponent

Cited by 29 publications

References 100 publications

Simulated shift work in rats perturbs multiscale regulation of locomotor activity

Simulated shift work in rats perturbs multiscale regulation of locomotor activity

Quantifying the degree of persistence in random amoeboid motion based on the Hurst exponent of fractional Brownian motion

Quantum probes for fractional Gaussian processes

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