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Register a new userSigmoids behaving badly: why they usually cannot predict the future as well as they seem to promise
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Added by
Stuart Armstrong
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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Sigmoids (AKA s-curves or logistic curves) are commonly used in a diverse spectrum of disciplines as models for time-varying phenomena showing initial acceleration followed by slowing: technology diffusion, cumulative cases of an epidemic, population growth towards a carrying capacity, etc. Existing work demonstrates that retrospective fit of data is often impressive. We show that in time series data, the future fit tends to be poor unless the data covers the entire range from before to after the inflection point. We discuss the theoretical reasons for this: the growth data provides little information about the damping term (and vice-versa). As a consequence, forecasting with sigmoids tends to be very unreliable. We suggest some practical approaches to improving the viability of forecasting sigmoid models.
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The mayfly nymph breathes under water through an oscillating array of wing-shaped tracheal gills. As the nymph grows, the kinematics of these gills change abruptly from rowing to flapping. The classical fluid dynamics approach to consider the mayfly nymph as a pumping device fails in giving clear reasons to this switch. In order to understand the whys and the hows of this switch between the two distinct kinematics, we analyze the problem under a Lagrangian viewpoint. We consider that a good Lagrangian transport that distributes and spreads water and dissolved oxygen well between and around the gills is the main goal of the gill motion. Using this Lagrangian approach we are able to provide the reason behind the switch from rowing to flapping that the mayfly nymph experiences as it grows. More precisely, recent and powerful tools from this Lagrangian approach are applied to in-sillico mayfly nymph experiments, where body shape, as well as, gill shapes, structures and kinematics are matched to those from in-vivo. In this letter, we show both qualitatively and quantitatively how the change of kinematics enables a better attraction, stirring and confinement of water charged of dissolved oxygen inside the gills area. From the computational velocity field we reveal attracting barriers to transport, i.e. attracting Lagrangian coherent structures, that form the transport skeleton between and around the gills. In addition, we quantify how well the fluid particles and consequently dissolved oxgen is spread and stirred inside the gills area.
The detection of GeV $gamma$-ray emission from Galactic novae by $Fermi$-LAT has become routine since 2010, and is generally associated with shocks internal to the nova ejecta. These shocks are also expected to heat plasma to $sim 10^7$ K, resulting in detectable X-ray emission. In this paper, we investigate 13 $gamma$-ray emitting novae observed with the Neil Gehrels $Swift$ Observatory, searching for 1-10 keV X-ray emission concurrent with $gamma$-ray detections. We also analyze $gamma$-ray observations of novae V407 Lup (2016) and V357 Mus (2018). We find that most novae do eventually show X-ray evidence of hot shocked plasma, but not until the $gamma$-rays have faded below detectability. We suggest that the delayed rise of the X-ray emission is due to large absorbing columns and/or X-ray suppression by corrugated shock fronts. The only nova in our sample with a concurrent X-ray/$gamma$-ray detection is also the only embedded nova (V407 Cyg). This exception supports a scenario where novae with giant companions produce shocks with external circumbinary material and are characterized by lower density environments, in comparison with novae with dwarf companions where shocks occur internal to the dense ejecta.
Privacy and nondiscrimination are related but different. We make this observation precise in two ways. First, we show that both privacy and nondiscrimination have t
Blobs, or quasi-spherical emission regions containing relativistic particles and magnetic fields, are often assumed ad hoc in emission models of relativistic astrophysical jets, yet their physical origin is still not well understood. Here, we employ a suite of large-scale two-dimensional particle-in-cell simulations in electron-positron plasmas to demonstrate that relativistic magnetic reconnection can naturally account for the formation of quasi-spherical plasmoids filled with high-energy particles and magnetic fields. Our simulations extend to unprecedentedly long temporal and spatial scales, so we can capture the asymptotic physics independently of the initial setup. We characterize the properties of the plasmoids that are continuously generated as a self-consistent by-product of the reconnection process: they are in rough energy equipartition between particles and magnetic fields; the upper energy cutoff of the plasmoid particle spectrum is proportional to the plasmoid width w, corresponding to a Larmor radius ~0.2 w; the plasmoids grow in size at ~0.1 of the speed of light, with most of the growth happening while they are still non-relativistic (first they grow); their growth is suppressed once they get accelerated to relativistic speeds by the field line tension, up to the Alfven speed (then they go). The largest plasmoids, whose typical recurrence interval is ~2.5 L/c, reach a characteristic size w ~ 0.2 L independently of the system length L, they have nearly isotropic particle distributions and they contain the highest energy particles, whose Larmor radius is ~0.03 L. The latter can be regarded as the Hillas criterion for relativistic reconnection. We briefly discuss the implications of our results for the high-energy emission from relativistic jets and pulsar winds.
The use of emergent constraints to quantify uncertainty for key policy relevant quantities such as Equilibrium Climate Sensitivity (ECS) has become increasingly widespread in recent years. Many researchers, however, claim that emergent constraints are inappropriate or even under-report uncertainty. In this paper we contribute to this discussion by examining the emergent constraints methodology in terms of its underpinning statistical assumptions. We argue that the existing frameworks are based on indefensible assumptions, then show how weakening them leads to a more transparent Bayesian framework wherein hitherto ignored sources of uncertainty, such as how reality might differ from models, can be quantified. We present a guided framework for the quantification of additional uncertainties that is linked to the confidence we can have in the underpinning physical arguments for using linear constraints. We provide a software tool for implementing our general framework for emergent constraints and use it to illustrate the framework on a number of recent emergent constraints for ECS. We find that the robustness of any constraint to additional uncertainties depends strongly on the confidence we can have in the underpinning physics, allowing a future framing of the debate over the validity of a particular constraint around the underlying physical arguments, rather than statistical assumptions.
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