Phase Space Structure, Attractor Dimension, Lyapunov Exponent and Nonlinear Prediction from Earth's Atmospheric Angular Momentum Time Series

Tiwari, R. K.; Rao, K. Nageswara

doi:10.1007/s000240050321

Cited by 6 publications

(2 citation statements)

References 35 publications

(59 reference statements)

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“…Stable or stochastic oscillations have a zero exponent, whereas chaotic systems show positive Lyapunov exponents. The use of this measure is widespread and has been used to reveal chaotic behavior in bacterial population dynamics (38), as well as economical and climatological systems (39,40). We analyzed 10 cells undergoing a mycorrhizal calcium response and found that 9 of the 10 cells showed positive Lyapunov exponents, indicating chaotic behavior (Fig.…”

Section: Rhizobial Bacteria and Mycorrhizal Fungi Induce Differentialmentioning

confidence: 99%

Differential and chaotic calcium signatures in the symbiosis signaling pathway of legumes

Kosuta

Hazledine²,

Sun³

et al. 2008

Proc. Natl. Acad. Sci. U.S.A.

252

215

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Understanding how the cell uses a limited set of proteins to transduce very different signals into specific cellular responses is a central goal of cell biology and signal transduction disciplines. Although multifunctionality in signal transduction is widespread, the mechanisms that allow differential modes of signaling in multifunctional signaling pathways are not well defined. In legume plants, a common symbiosis signaling pathway composed of at least seven proteins mediates infection by both mycorrhizal fungi and rhizobial bacteria. Here we show that the symbiosis signaling pathway in legumes differentially transduces both bacterial and fungal signals (inputs) to generate alternative calcium responses (outputs). We show that these differential calcium responses are dependent on the same proteins, DMI1 and DMI2, for their activation, indicating an inherent flexibility in this signaling pathway. By using Lyapunov and other mathematical analyses, we discovered that both bacterial-induced and fungalinduced calcium responses are chaotic in nature. Chaotic systems require minimal energy to produce a wide spectrum of outputs in response to marginally different inputs. The flexibility provided by chaotic systems is consistent with the need to transduce two different signals, one from rhizobial bacteria and one from mycorrhizal fungi, by using common components of a single signaling pathway.chaos ͉ mycorrhization ͉ nodulation

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Section: Rhizobial Bacteria and Mycorrhizal Fungi Induce Differentialmentioning

confidence: 99%

Differential and chaotic calcium signatures in the symbiosis signaling pathway of legumes

Kosuta

Hazledine²,

Sun³

et al. 2008

Proc. Natl. Acad. Sci. U.S.A.

252

215

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show abstract

“…This particular method of nonlinear forecasting is relatively robust and works well on natural data. Several studies (MCCLOSKEY et al, 1991;MCCLOSKEY, 1993;TSONIS and ELSNER 1992;TIWARI and RAO, 1998) demonstrated the applicability of this technique for multidimensional data using the synthetic as well as actual time series, aiming to distinguish chaos from stochastic/random fractals.…”

Section: Nonlinear Forecasting Techniquementioning

confidence: 99%

Characterization of Earthquake Dynamics in Northeastern India Regions: A Modern Nonlinear Forecasting Approach

Tiwari

Lakshmi

Rao

2004

Pure and Applied Geophysics

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The Northeastern India (NEI) region, is seismotectonically one of the most active regions of the world. Earlier studies of NEI earthquake data have provided contrasting evidence for the presence of randomness and low-dimensional ''strange attractor.'' Here, in the present study, we assess the dimensionality of an earthquake-generating mechanism by nonlinear predictability analyses on phase portrait constructed by monthly frequency earthquake time series which was obtained from the NOAA catalogue. The result of nonlinear forecasting analyses suggests that the earthquake processes in the NEI region evolve on a non-random high-dimensional chaotic system. Such a complex high-dimensional earthquake behavior is indicative of heterogeneous geological structures in which weak fault zones and/or individual fault interactions might have strength fluctuations due to pore pressure variation. Further, K 2 entropy analysis was performed to isolate the non-random component from the data. The analysis reveals a quasi-coherent time structure, (K 2 % 0.08/month) which corresponds to a seasonal time scale of about 12 months. We argue that stochastic resonance created by seasonality bias may have combined with noise to affect the pore pressure variation leading to subsequent earthquake triggering. It is interesting to note that most earthquakes and swarm activities occurred during or after the monsoon season. Geological and geophysical evidence also reconciles with the above view. Evidence for high-dimensional chaos associated with ''seasonal'' bias in the NEI region may provide useful constraints for testing models and criteria to assess earthquake hazards on a more rigorous and quantitative basis.

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Advances in Geo-Time Series Modelling

Tiwari

Rekapalli

2021

Journal of the Geological Society of India

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Recent advances in geo-time series modelling are briefly presented. These progressive developments and imminent applications in the data-driven research have come across three main categories of investigation efforts (i) Classical to recent advances in spectral analyses and their applications on some very significant geophysical/geological time series. Specially, applications of modern multi-taper methods of spectral analysis (MTM) and singular spectral analysis (SSA) techniques based filtering are discussed. Applications on 3D seismic reflection data de-noising using multi-channel SSA along with significant results are demonstrated. (ii) Methods of nonlinear time series analyses and physical concept of fractal and chaos are enumerated and relevance of chaos in complex geophysical and geological time series modelling are discussed (iii) The upcoming field of research in Machine learning (ML) based artificial neural network (ANN) and Deep Learning (DL) along with pertinent applications on variety of geophysical data, such well-log, ground water, gravity, seismic / seismological data etc., are presented and discussed.

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Phase Space Structure, Attractor Dimension, Lyapunov Exponent and Nonlinear Prediction from Earth's Atmospheric Angular Momentum Time Series

Cited by 6 publications

References 35 publications

Differential and chaotic calcium signatures in the symbiosis signaling pathway of legumes

Differential and chaotic calcium signatures in the symbiosis signaling pathway of legumes

Characterization of Earthquake Dynamics in Northeastern India Regions: A Modern Nonlinear Forecasting Approach

Advances in Geo-Time Series Modelling

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