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In the submodular ranking (SR) problem, the input consists of a set of submodular functions defined on a ground set of elements. The goal is to order elements for all the functions to have value above a certain threshold as soon on average as possible, assuming we choose one element per time. The problem is flexible enough to capture various applications in machine learning, including decision trees. This paper considers the min-max version of SR where multiple instances share the ground set. With the view of each instance being associated with an agent, the min-max problem is to order the common elements to minimize the maximum objective of all agents---thus, finding a fair solution for all agents. We give approximation algorithms for this problem and demonstrate their effectiveness in the application of finding a decision tree for multiple agents.

In this work, the Thermosphere‐Ionosphere‐Electrodynamics General Circulation Model is used to investigate the responses of ionospheric electrodynamic processes to the solar flares at the flare peaks and the underlying physical mechanisms on September 6 and 10, 2017. Simulations show that solar flares increased global daytime currents and reduced the eastward electric fields during the daytime from the equator to middle latitudes. Furthermore, westward equatorial electric fields and equatorial counter electrojets occurred in the early morning. At the flare peak, these electrodynamic responses are predominantly related to the enhanced E‐region conductivity by flares, as the responses of neutral winds and F‐region conductivity to flares are negligible. Specifically, the Cowling conductance enhancement is not the major process causing the reduction of zonal electric fields. This electric field reduction is primarily associated with the decrease of the ratio between the field line‐integrated wind‐driven currents and the conductance. The flare‐induced conductivity enhancement is larger but the background wind speed is smaller in the E‐region than in the F‐region, as a result, the increase of total integrated wind‐driven currents is less than the conductance enhancement.

Ionospheric day‐to‐day variability is ubiquitous, even under undisturbed geomagnetic and solar conditions. In this paper, quiet‐time day‐to‐day variability of equatorial vertical E × B drift is investigated using observations from ROCSAT‐1 satellite and the Whole Atmosphere Community Climate Model with thermosphere and ionosphere eXtension (WACCM‐X) v2.1 simulations. Both observations and model simulations illustrate that the day‐to‐day variability reaches the maximum at dawn, and the variability of dawn drift is largest around June solstice at ~90–180°W. However, there are significant challenges to reproduce the observed magnitude of the variability and the longitude distributions at other seasons. Using a standalone electro‐dynamo model, we find that the day‐to‐day variability of neutral winds in the E‐region (≤~130 km) is the primary driver of the day‐to‐day variability of dawn drift. Ionospheric conductivity modulates the drift variability responses to the E‐region wind variability, thereby determining its strength as well as its seasonal and longitudinal variations. Further, the day‐to‐day variability of dawn drift induced by individual tidal components of winds in June are examined: DW1, SW2, D0, and SW1 are the most important contributors.