Circadian rhythms become less dominant and less regular with chronic-degenerative disease, such that to accurately assess these pathological conditions it is important to quantify not only periodic characteristics but also more irregular aspects of the corresponding time series. Novel data-adaptive techniques, such as singular spectrum analysis (SSA), allow for the decomposition of experimental time series, in a model-free way, into a trend, quasiperiodic components and noise fluctuations. We compared SSA with the traditional techniques of cosinor analysis and intradaily variability using 1-week continuous actigraphy data in young adults with acute insomnia and healthy age-matched controls. The findings suggest a small but significant delay in circadian components in the subjects with acute insomnia, i.e. a larger acrophase, and alterations in the day-to-day variability of acrophase and amplitude. The power of the ultradian components follows a fractal 1/f power law for controls, whereas for those with acute insomnia this power law breaks down because of an increased variability at the 90min time scale, reminiscent of Kleitman’s basic rest-activity (BRAC) cycles. This suggests that for healthy sleepers attention and activity can be sustained at whatever time scale required by circumstances, whereas for those with acute insomnia this capacity may be impaired and these individuals need to rest or switch activities in order to stay focused. Traditional methods of circadian rhythm analysis are unable to detect the more subtle effects of day-to-day variability and ultradian rhythm fragmentation at the specific 90min time scale.

Sustainability is a key concept in economic and policy debates. Nevertheless, it is usually treated only in a qualitative way and has eluded quantitative analysis. Here, we propose a sustainability index based on the premise that sustainable systems do not lose or gain Fisher Information over time. We test this approach using time series data from the AmeriFlux network that measures ecosystem respiration, water and energy fluxes in order to elucidate two key sustainability features: ecosystem health and stability. A novel definition of ecosystem health is developed based on the concept of criticality, which implies that if a system’s fluctuations are scale invariant then the system is in a balance between robustness and adaptability. We define ecosystem stability by taking an information theory approach that measures its entropy and Fisher information. Analysis of the Ameriflux consortium big data set of ecosystem respiration time series is contrasted with land condition data. In general we find a good agreement between the sustainability index and land condition data. However, we acknowledge that the results are a preliminary test of the approach and further verification will require a multi-signal analysis. For example, high values of the sustainability index for some croplands are counter-intuitive and we interpret these results as ecosystems maintained in artificial health due to continuous human-induced inflows of matter and energy in the form of soil nutrients and control of competition, pests and disease.

We present 3D, adaptive mesh refinement simulations of G2, a cloud of gas moving in a highly eccentric orbit towards the galactic center. We assume that G2 originates from a stellar wind interacting with the environment of the Sgr A* black hole. The stellar wind forms a cometary bubble which becomes increasingly elongated as the star approaches periastron. A few months after periastron passage, streams of material begin to accrete on the central black hole with accretion rateṡ M ∼ 10 −8 M ⊙ yr −1 . Predicted Brγ emission maps and position-velocity diagrams show an elongated emission resembling recent observations of G2. A large increase in luminosity is predicted by the emission coming from the shocked wind region during periastron passage. The observations, showing a constant Brγ luminosity, remain puzzling, and are explained here assuming that the emission is dominated by the free-wind region. The observed Brγ luminosity (∼ 8 × 10 30 erg s −1 ) is reproduced by a model with a v w = 50 km s −1 wind velocity and a 10 −7 M ⊙ yr −1 mass loss rate if the emission comes from the shocked wind. A faster and less dense wind reproduces the Brγ luminosity if the emission comes from the inner, free wind region. The extended cometary wind bubble, largely destroyed by the tidal interaction with the black hole, reforms a few years after periastron passage. As a result, the Brγ emission is more compact after periastron passage.