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

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

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

Anticipating manic and depressive transitions in patients with bipolar disorder using early warning signals

Background In bipolar disorder treatment, accurate episode prediction is paramount but remains difficult. A novel idiographic approach to prediction is to monitor generic early warning signals (EWS), which may manifest in symptom dynamics. EWS could thus form personalized alerts in clinical care. The present study investigated whether EWS can anticipate manic and depressive transitions in individual patients with bipolar disorder. Methods Twenty bipolar type I/II patients (with >= 2 episodes in the previous year) participated in ecological momentary assessment (EMA), completing five questionnaires a day for four months (Mean = 491 observations per person). Transitions were determined by weekly completed questionnaires on depressive (Quick Inventory for Depressive Symptomatology Self-Report) and manic (Altman Self-Rating Mania Scale) symptoms. EWS (rises in autocorrelation at lag-1 and standard deviation) were calculated in moving windows over 17 affective and symptomatic EMA states. Positive and negative predictive values were calculated to determine clinical utility. Results Eleven patients reported 1-2 transitions. The presence of EWS increased the probability of impending depressive and manic transitions from 32-36% to 46-48% (autocorrelation) and 29-41% (standard deviation). However, the absence of EWS could not be taken as a sign that no transition would occur in the near future. The momentary states that indicated nearby transitions most accurately (predictive values: 65-100%) were full of ideas, worry, and agitation. Large individual differences in the utility of EWS were found. Conclusions EWS show theoretical promise in anticipating manic and depressive transitions in bipolar disorder, but the level of false positives and negatives, as well as the heterogeneity within and between individuals and preprocessing methods currently limit clinical utility

Efficacy of early warning signals and spectral periodicity for predicting transitions in bipolar patients:An actigraphy study

Early-warning signals (EWS) have been successfully employed to predict transitions in research fields such as biology, ecology, and psychiatry. The predictive properties of EWS might aid in foreseeing transitions in mood episodes (i.e. recurrent episodes of mania and depression) in bipolar disorder (BD) patients. We analyzed actigraphy data assessed during normal daily life to investigate the feasibility of using EWS to predict mood transitions in bipolar patients. Actigraphy data of 15 patients diagnosed with BD Type I collected continuously for 180 days were used. Our final sample included eight patients that experienced a mood episode, three manic episodes and five depressed episodes. Actigraphy data derived generic EWS (variance and kurtosis) and context-driven EWS (autocorrelation at lag-720) were used to determine if these were associated to upcoming bipolar episodes. Spectral analysis was used to predict changes in the periodicity of the sleep/wake cycle. The study procedures were pre-registered. Results indicated that in seven out of eight patients at least one of the EWS did show a significant change-up till four weeks before episode onset. For the generic EWS the direction of change was always in the expected direction, whereas for the context-driven EWS the observed effect was often in the direction opposite of what was expected. The actigraphy data derived EWS and spectral analysis showed promise for the prediction of upcoming transitions in mood episodes in bipolar patients. Further studies into false positive rates are suggested to improve effectiveness for EWS to identify upcoming bipolar episode onsets

Early warning signals in psychopathology:what do they tell?

BACKGROUND: Despite the increasing understanding of factors that might underlie psychiatric disorders, prospectively detecting shifts from a healthy towards a symptomatic state has remained unattainable. A complex systems perspective on psychopathology implies that such symptom shifts may be foreseen by generic indicators of instability, or early warning signals (EWS). EWS include, for instance, increasing variability, covariance, and autocorrelation in momentary affective states-of which the latter was studied. The present study investigated if EWS predict (i) future worsening of symptoms as well as (ii) the type of symptoms that will develop, meaning that the association between EWS and future symptom shifts would be most pronounced for congruent affective states and psychopathological domains (e.g., feeling down and depression). METHODS: A registered general population cohort of adolescents (mean age 18 years, 36% male) provided ten daily ratings of their affective states for 6 consecutive days. The resulting time series were used to compute EWS in feeling down, listless, anxious, not relaxed, insecure, suspicious, and unwell. At baseline and 1-year follow-up, symptom severity was assessed by the Symptom Checklist-90 (SCL-90). We selected four subsamples of participants who reported an increase in one of the following SCL-90 domains: depression (N = 180), anxiety (N = 192), interpersonal sensitivity (N = 184), or somatic complaints (N = 166). RESULTS: Multilevel models showed that EWS in feeling suspicious anticipated increases in interpersonal sensitivity, as hypothesized. EWS were absent for other domains. While the association between EWS and symptom increases was restricted to the interpersonal sensitivity domain, post hoc analyses showed that symptom severity at baseline was related to heightened autocorrelations in congruent affective states for interpersonal sensitivity, depression, and anxiety. This pattern replicated in a second, independent dataset. CONCLUSIONS: The presence of EWS prior to symptom shifts may depend on the dynamics of the psychopathological domain under consideration: for depression, EWS may manifest only several weeks prior to a shift, while for interpersonal sensitivity, EWS may already occur 1 year in advance. Intensive longitudinal designs where EWS and symptoms are assessed in real-time are required in order to determine at what timescale and for what type of domain EWS are most informative of future psychopathology