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Recent observations have revealed a trove of unexpected morphological features in many of the Milky Way’s stellar streams. Explanations for such features include time-dependent deformations of the Galactic gravitational potential, local disruptions induced by dark matter substructure, and special configurations of the streams’ progenitors. In this paper, we study how these morphologies can also arise in certain static, nonspherical gravitational potentials that host a subset of resonantly trapped orbit families. The transitions, or separatrices, between these orbit families mark abrupt discontinuities in the orbital structure of the potential. We develop a novel numerical approach for measuring the libration frequencies of resonant and near-resonant orbits and apply it to study the evolution of stellar streams on these orbits. We reveal two distinct morphological features that arise in streams on near-resonant orbits: fans, which come about due to a large spread in the libration frequencies near a separatrix, and bifurcations, which arise when a separatrix splits the orbital distribution of the stellar stream between two (or more) distinct orbit families. We demonstrate that these effects can arise in some Milky Way streams for certain choices of the dark matter halo potential and discuss how this might be used to probe and constrain the global shape of the Milky Way’s gravitational potential.

 

Artificial intelligence (AI) systems have begun to be deployed in high-stakes contexts, including autonomous driving and medical diagnosis. In contexts such as these, the consequences of system failures can be devastating. It is therefore vital that researchers and policy-makers have a full understanding of the capabilities and weaknesses of AI systems so that they can make informed decisions about where these systems are safe to use and how they might be improved. Unfortunately, current approaches to AI evaluation make it exceedingly difficult to build such an understanding, for two key reasons. First, aggregate metrics make it hard to predict how a system will perform in a particular situation. Second, the instance-by-instance evaluation results that could be used to unpack these aggregate metrics are rarely made available ( 1 ). Here, we propose a path forward in which results are presented in more nuanced ways and instance-by-instance evaluation results are made publicly available. 

When human adults make decisions (e.g., wearing a seat belt), we often consider the negative consequences that would ensue if our actions were to fail, even if we have never experienced such a failure. Do the same considerations guide our understanding of other people's decisions? In this paper, we investigated whether adults, who have many years of experience making such decisions, and 6‐ and 7‐year‐old children, who have less experience and are demonstrably worse at judging the consequences of their own actions, conceive others' actions as motivated both by reward (how good reaching one's intended goal would be), and by what we call “danger” (how badly one's action could end). In two pre‐registered experiments, we tested whether adults and 6‐ and 7‐year‐old children tailor their predictions and explanations of an agent's action choices to the specific degree of danger and reward entailed by each action. Across four different tasks, we found that children and adults expected others to negatively appraise dangerous situations and minimize the danger of their actions. Children's and adults' judgments varied systematically in accord with both the degree of danger the agent faced and the value the agent placed on the goal state it aimed to achieve. However, children did not calibrate their inferences abouthow muchan agent valued the goal state of a successful action in accord with the degree of danger the action entailed, and adults calibrated these inferences more weakly than inferences concerning the agent's future action choices. These results suggest that from childhood, people use a degree of danger and reward to make quantitative, fine‐grained explanations and predictions about other people's behavior, consistent with computational models on theory of mind that contain continuous representations of other agents' action plans.

 

ABSTRACT Flattened axisymmetric galactic potentials are known to host minor orbit families surrounding orbits with commensurable frequencies. The behaviour of orbits that belong to these orbit families is fundamentally different than that of typical orbits with non-commensurable frequencies. We investigate the evolution of stellar streams on orbits near the boundaries between orbit families (separatrices) in a flattened axisymmetric potential. We demonstrate that the separatrix divides these streams into two groups of stars that belong to two different orbit families, and that as a result, these streams diffuse more rapidly than streams that evolve elsewhere in the potential. We utilize Hamiltonian perturbation theory to estimate both the time-scale of this effect and the likelihood of a stream evolving close enough to a separatrix to be affected by it. We analyse two prior reports of stream-fanning in simulations with triaxial potentials, and conclude that at least one of them is caused by separatrix divergence. These results lay the foundation for a method of mapping the orbit families of galactic potentials using the morphology of stellar streams. Comparing these predictions with the currently known distribution of streams in the Milky Way presents a new way of constraining the shape of our Galaxy’s potential and distribution of dark matter.