Hilbert transform‐based time‐series analysis of the circadian gene regulatory network

Shiju, S; Sriram, K.

doi:10.1049/iet-syb.2018.5088

Cited by 3 publications

(2 citation statements)

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“…There are a variety of ways to measure phase, as described in an accessible introduction to phase measures 31 . In addition to its independence from the periodogram, the phase measure used here and elsewhere was used to assess whether or not synchronization is taking place between single cells experiencing a common driving light signal 5,30,[42][43][44][45] (see "Materials and methods" for a definition of phase).…”

Section: Scientific Reportsmentioning

confidence: 99%

Identifying a stochastic clock network with light entrainment for single cells of Neurospora crassa

Caranica

Al-Omari

Schüttler

et al. 2020

Sci Rep

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Stochastic networks for the clock were identified by ensemble methods using genetic algorithms that captured the amplitude and period variation in single cell oscillators of Neurosporacrassa. The genetic algorithms were at least an order of magnitude faster than ensemble methods using parallel tempering and appeared to provide a globally optimum solution from a random start in the initial guess of model parameters (i.e., rate constants and initial counts of molecules in a cell). The resulting goodness of fit $${x}^{2}$$ x 2 was roughly halved versus solutions produced by ensemble methods using parallel tempering, and the resulting $${x}^{2}$$ x 2 per data point was only $${\chi }^{2}/n$$ χ 2 / n = 2,708.05/953 = 2.84. The fitted model ensemble was robust to variation in proxies for “cell size”. The fitted neutral models without cellular communication between single cells isolated by microfluidics provided evidence for only one Stochastic Resonance at one common level of stochastic intracellular noise across days from 6 to 36 h of light/dark (L/D) or in a D/D experiment. When the light-driven phase synchronization was strong as measured by the Kuramoto (K), there was degradation in the single cell oscillations away from the stochastic resonance. The rate constants for the stochastic clock network are consistent with those determined on a macroscopic scale of 107 cells.

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Section: Scientific Reportsmentioning

confidence: 99%

Identifying a stochastic clock network with light entrainment for single cells of Neurospora crassa

Caranica

Al-Omari

Schüttler

et al. 2020

Sci Rep

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“…Generally, this abrupt change of phase difference is called phase slip. 76,77 So, to verify the appearance of the phase slip, we first calculate the instantaneous phase of the ac torque τ sin(ωt + φ) using the Hilbert Transform 78 method and then calculate its difference with the system's phase θ , and finally, we plot the phase difference with respect to time in the lower panel of Fig. 5.…”

Section: Articlementioning

confidence: 99%

Extreme rotational events in a forced-damped nonlinear pendulum

Pal

Ray

Chowdhury³

et al. 2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Since Galileo’s time, the pendulum has evolved into one of the most exciting physical objects in mathematical modeling due to its vast range of applications for studying various oscillatory dynamics, including bifurcations and chaos, under various interests. This well-deserved focus aids in comprehending various oscillatory physical phenomena that can be reduced to the equations of the pendulum. The present article focuses on the rotational dynamics of the two-dimensional forced-damped pendulum under the influence of the ac and dc torque. Interestingly, we are able to detect a range of the pendulum’s length for which the angular velocity exhibits a few intermittent extreme rotational events that deviate significantly from a certain well-defined threshold. The statistics of the return intervals between these extreme rotational events are supported by our data to be spread exponentially at a specific pendulum’s length beyond which the external dc and ac torque are no longer sufficient for a full rotation around the pivot. The numerical results show a sudden increase in the size of the chaotic attractor due to interior crisis, which is the source of instability that is responsible for triggering large amplitude events in our system. We also notice the occurrence of phase slips with the appearance of extreme rotational events when the phase difference between the instantaneous phase of the system and the externally applied ac torque is observed.

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