Origin of chaos in the Prometheus–Pandora system

We demonstrate that the chaotic orbits of Prometheus and Pandora are due to interactions associated with the 121:118 mean motion resonance. Differential precession splits this resonance into a quartet of components equally spaced in frequency. Libration widths of the individual components exceed the splitting resulting in resonance overlap which causes the chaos. A single degree of freedom model captures the essential features of the chaotic dynamics. Mean motions of Prometheus and Pandora wander chaotically in zones of width 1.8 deg yr^−1 and 3.1 deg yr^−1, respectively

Dynamical selection of Nash equilibria using Experience Weighted Attraction Learning: emergence of heterogeneous mixed equilibria

We study the distribution of strategies in a large game that models how agents choose among different double auction markets. We classify the possible mean field Nash equilibria, which include potentially segregated states where an agent population can split into subpopulations adopting different strategies. As the game is aggregative, the actual equilibrium strategy distributions remain undetermined, however. We therefore compare with the results of Experience-Weighted Attraction (EWA) learning, which at long times leads to Nash equilibria in the appropriate limits of large intensity of choice, low noise (long agent memory) and perfect imputation of missing scores (fictitious play). The learning dynamics breaks the indeterminacy of the Nash equilibria. Non-trivially, depending on how the relevant limits are taken, more than one type of equilibrium can be selected. These include the standard homogeneous mixed and heterogeneous pure states, but also \emph{heterogeneous mixed} states where different agents play different strategies that are not all pure. The analysis of the EWA learning involves Fokker-Planck modeling combined with large deviation methods. The theoretical results are confirmed by multi-agent simulations.Comment: 35 pages, 16 figure

Chaotic motions of Prometheus and Pandora

Recent HST images of the Saturnian satellites Prometheus and Pandora show that their longitudes deviate from predictions of ephemerides based on Voyager images. Currently Prometheus is lagging and Pandora leading these predictions by somewhat more than 20◦. We show that these discrepancies are fully accounted for by gravitational interactions between the two satellites. These peak every 24.8 d at conjunctions and excite chaotic perturbations. The Lyapunov exponent for the Prometheus-Pandora system is of order 0.35 yr^−1 for satellite masses based on a nominal density of 1.3 g cm^−3. Interactions are strongest when the orbits come closest together. This happens at intervals of 6.2 yr when their apses are anti-aligned. In this context we note the sudden changes of opposite signs in the mean motions of Prometheus and Pandora at the end of 2000 occured shortly after their apsidal lines were anti-aligned

The effect of prototyping material on verbal and non-verbal behaviours in collaborative design tasks

This paper reports a study of 23 controlled experiments, with a total of 99 individual tasks, between pairs of designers collaborating to solve a simple design task using four different types of prototyping media. The aim of the study was to correlate verbal and non-verbal behaviours across different types of media with a range of measurement indicators. Using innovative movement trail images we show how collaborative sketching activity results in attenuated use of interpersonal collaborative space when compared with cardboard, clay, and Lego, which provoked intensive collaboration. Furthermore, the sketching (control) condition resulted in pre-conceived ideas being executed when compared with the three-dimensional media, where ideas emerged through collaboration. This finding suggests that increased creativity in design can result through the careful choice of prototyping media at the beginning of the design process

Lepskii Principle in Supervised Learning

In the setting of supervised learning using reproducing kernel methods, we propose a data-dependent regularization parameter selection rule that is adaptive to the unknown regularity of the target function and is optimal both for the least-square (prediction) error and for the reproducing kernel Hilbert space (reconstruction) norm error. It is based on a modified Lepskii balancing principle using a varying family of norms

Construction and performance of a novel capture-mark-release moth trap

Mark-recapture studies can provide important information about moth movement as well as habitat preference across a landscape, but to date, such studies tend to be species-specific or require labor-intensive methodologies. To address this challenge, we designed a capture-mark-release-trap (CMRT) featuring a cooling unit attached to a black light trap. The CMRT captures and incapacitates moths throughout the night until the morning, when they can be marked on-site and released. Moths captured with the CMRT during summer of 2016 had a recapture rate of 1.6%, similar to those of previous studies. Importantly, because moths are immobilized by the CMRT, they can be handled and marked with ease, reducing the opportunities to damage specimens prior to release. The CMRT trap can capture a wide array of moth species and may facilitate an increase in the monitoring of moth movement across landscapes

Hot Water Dipping in Northern Germany- on farm results after four years of scientific work

In general, organic grown apples (Malus x domestica Borkh.) are not treated with chemical fungicides to pre-vent storage decay and these fruits may suffer up to 30% decay during storage. Preliminary experiments had shown that hot water dipping of apples may be an alternative. To inhibit Gloeosporium rot (Pezicula alba, P. malicortis) water temperature may be of about 50°C and dipping time from 60 sec up to 240 sec. The objec-tive was to determinate the suitable hot water treatment that prevent decay incidence and maintain fruit qual-ity (firmness, scale symptoms). In between the years 2002 and 2005 the test were repeated and a recom-mendation for the apple varieties in the area Northern Germany was elaborated

Early motor trajectories predict motor but not cognitive function in preterm- and term-born adults without pre-existing neurological conditions

Very preterm (VP; 0.05). Motor problems in childhood were homotypically associated with poorer motor competence in adulthood. Similarly, early cognitive problems were homotypically associated with adult cognitive outcomes. Thus, both motor and cognitive function should be assessed in routine follow-up during childhood