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Abstract Because of the extreme purity, lack of disorder, and complex order parameter, the first-order superfluid 3 He A–B transition is the leading model system for first order transitions in the early universe. Here we report on the path dependence of the supercooling of the A phase over a wide range of pressures below 29.3 bar at nearly zero magnetic field. The A phase can be cooled significantly below the thermodynamic A–B transition temperature. While the extent of supercooling is highly reproducible, it depends strongly upon the cooling trajectory: The metastability of the A phase is enhanced by transiting through regions where the A phase is more stable. We provide evidence that some of the additional supercooling is due to the elimination of B phase nucleation precursors formed upon passage through the superfluid transition. A greater understanding of the physics is essential before 3 He can be exploited to model transitions in the early universe. 

Abstract Channel planform patterns arise from internal dynamics of sediment transport and fluid flow in rivers and are affected by external controls such as valley confinement. Understanding whether these channel patterns are preserved in the rock record has critical implications for our ability to constrain past environmental conditions. Rivers are preserved as channel belts, which are one of the most ubiquitous and accessible parts of the sedimentary record, yet the relationship between river and channel-belt planform patterns remains unquantified. We analyzed planform patterns of rivers and channel belts from 30 systems globally. Channel patterns were classified using a graph theory-based metric, the Entropic Braided Index (eBI), which quantifies the number of river channels by considering the partitioning of water and sediment discharge. We find that, after normalizing by river size, channel-belt width and wavelength, amplitude, and curvature of the belt edges decrease with increasing river channel number (eBI). Active flow in single-channel rivers occupies as little as 1% of the channel belt, while in multichannel rivers it can occupy >50% of the channel belt. Moreover, we find that channel patterns lie along a continuum of channel numbers. Our findings have implications for studies on river and floodplain interaction, storage timescales of floodplain sediment, and paleoenvironmental reconstruction. 

Algorithmic decisions made by machine learning models in high-stakes domains may have lasting impacts over time. However, naive applications of standard fairness criterion in static settings over temporal domains may lead to delayed and adverse effects. To understand the dynamics of performance disparity, we study a fairness problem in Markov decision processes (MDPs). Specifically, we propose return parity, a fairness notion that requires MDPs from different demographic groups that share the same state and action spaces to achieve approximately the same expected time-discounted rewards. We first provide a decomposition theorem for return disparity, which decomposes the return disparity of any two MDPs sharing the same state and action spaces into the distance between group-wise reward functions, the discrepancy of group policies, and the discrepancy between state visitation distributions induced by the group policies. Motivated by our decomposition theorem, we propose algorithms to mitigate return disparity via learning a shared group policy with state visitation distributional alignment using integral probability metrics. We conduct experiments to corroborate our results, showing that the proposed algorithm can successfully close the disparity gap while maintaining the performance of policies on two real-world recommender system benchmark datasets.