Fractal Measures and Nonlinear Dynamics of Overcontact Binaries

Overcontact binary stars are systems of two stars where the component stars are in contact with each other. This implies that they share a common envelope of gas. In this work we seek signatures of nonlinearity and chaos in these stars by using time series analysis techniques. We use three main techniques, namely the correlation dimension,f (\alpha) spectrum and the bicoherence. The former two are calculated from the reconstructed dynamics, while the latter is calculated from the Fourier transforms of the time series of intensity variations(light curves) of these stars. Our dataset consists of data from 463 overcontact binary stars in the Kepler field of view [1]. Our analysis indicates nonlinearity and signatures of chaos in almost all the light curves. We also explore whether the underlying nonlinear properties of the stars are related to their physical properties like fill-out-factor, a measure of the extend of contact between the components of an overcontact binary system . We observe that significant correlations exist between the fill out factor and the nonlinear quantifiers. This correlation is more pronounced in specific subcategories constructed based on the mass ratios and effective temperatures of the binaries. The correlations observed can be indicative of variations in the nonlinear properties of the star as it ages. We believe that this study relating nonlinear and astrophysical properties of binary stars is the first of its kind and is an important starting point for such studies in other astrophysical objects displaying nonlinear dynamical behaviour.Comment: 17 pages, 12 figures, submitted to Communications in Nonlinear Science and Numerical Simulatio

Early warning signals for critical transitions in complex systems

In this review, we present the different measures of early warning signals that can indicate the occurrence of critical transitions in complex systems. We start with the mechanisms that trigger critical transitions, how they relate to warning signals and the methods used to detect early warning signals (EWS) for sudden transitions or tipping. We discuss briefly a few applications in real systems in this context, like transitions in ecology, climate and environment, medicine, epidemics, finance and engineering. Towards the end, we mention the issues in detecting EWS in specific applications and our perspective on future trends in this area, especially related to sudden transitions in the dynamics of connected systems on complex networks.Comment: 35 pages, 11 figure

Early warning signals indicate a critical transition in Betelgeuse

Critical transitions occur in complex dynamical systems, when the system dynamics undergoes a regime shift. These can often occur with little change in the mean amplitude of system response prior to the actual time of transition. The recent dimming and brightening event in Betelgeuse occured as a sudden shift in the brightness and has been the subject of much debate. Internal changes or an external dust cloud have been suggested as reasons for this change in variability. We examine whether the dimming and brightening event of 2019-20 could be due to a critical transition in the pulsation dynamics of Betelgeuse, by studying the characteristics of the light curve prior to transition. We calculate the quantifiers hypothesised to rise prior to a critical transition for the light curve of Betelgeuse upto the dimming event of 2019-20. These include the autocorrelation at lag-1, variance and the spectral coefficient calculated from detrended fluctation analysis (DFA), apart from two measures that quantify the recurrence properties of the light curve. Significant rises are confirmed using the Mann-Kendall trend test. We see a significant increase in all quantifiers (p < 0.05) prior to the dimming event of 2019-20. This suggests that the event was a critical transition related to the underlying nonlinear dynamics of the star. Together with results that suggests minimal change in $T_{eff}$ and infra-red flux, a critical transition in the pulsation dynamics could be a possible reason for the unprecedented dimming of Betelgeuse. The rise in the studied quantifiers prior to the dimming event, supports this possibility.Comment: 8 pages, 8 figure

A hybrid neural ordinary differential equation model of the cardiovascular system

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Forecasting of arecanut market price in north eastern India: ARIMA modelling approach

The paper deals with forecasting of minimum, maximum and average arecanut (Areca catechu L.) prices in the major arecanut markets of the Assam as well as Meghalaya based on the monthly price data. Monthly minimum, maximum, and average market price data of arecanut (in Rs./quintal) for the period May-2003 to March-2012 (for Assam) and February-2003 to March-2012 (for Meghalaya) were used. Box-Jenkins autoregressive integrated moving average (ARIMA) methodology was adopted for developing the models. An interrupted time-series model was also applied to resolve the problem of intervention point (October-2011) for Meghalaya price data. The proposed models were ARIMA (1, 0, 1), ARIMA (1, 1, 1), ARIMA (0, 1, 1) (for Assam market price data series) and, log ARIMA (0, 1, 1), log ARIMA (1, 0, 1) with linear trend and a man-made intervention (Oct-2011) and log ARIMA (0, 1, 1) with linear trend and a manmade intervention (Oct-2011) (for Meghalaya market price data series) for minimum, maximum, and average monthly price series, respectively

A variable heart rate multi-compartmental coupled model of the cardiovascular and respiratory systems

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A variable heart rate multi-compartmental coupled model of the cardiovascular and respiratory systems

Current mathematical models of the cardiovascular system that are based on systems of ordinary differential equations are limited in their ability to mimic important features of measured patient data, such as variable heart rates (HR). Such limitations present a significant obstacle in the use of such models for clinical decision-making, as it is the variations in vital signs such as HR and systolic and diastolic blood pressure that are monitored and recorded in typical critical care bedside monitoring systems. In this paper, novel extensions to well-established multi-compartmental models of the cardiovascular and respiratory systems are proposed that permit the simulation of variable HR. Furthermore, a correction to current models is also proposed to stabilize the respiratory behaviour and enable realistic simulation of vital signs over the longer time scales required for clinical management. The results of the extended model developed here show better agreement with measured bio-signals, and these extensions provide an important first step towards estimating model parameters from patient data, using methods such as neural ordinary differential equations. The approach presented is generalizable to many other similar multi-compartmental models of the cardiovascular and respiratory systems

Predicting recurrence of depression using cardiac complexity in individuals tapering antidepressants

Funding Information: We would like to thank GM Bloem, D Sloohof, G Arts, and E van den Kieboom for their work on (pre-)processing the physiological data. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (ERC-CoG-2015; No. 681466 to M Wichers). The Cortrium monitors were kindly provided by the iLab of the Department of Psychiatry of the University Medical Center Groningen (UMCG, http://www.ilab-psychiatry.nl ).Peer reviewe