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Axion-like degrees of freedom generally interact with fermions through a shift symmetric coupling. As a consequence, a time-dependent axion will lead to the generation of fermions by amplifying their vacuum fluctuations. We provide the formulae that allow one to determine the spectra of produced fermions in a generic Friedmann-Lemaître-Robertson-Walker Universe with flat spatial slices. Then we derive simple approximate formulae for the spectra of the produced fermions, as a function of the model parameters, in the specific cases of a radiation- and a matter-dominated Universe, in the regime in which the backreaction of the produced fermions on the axionic background can be neglected. 

Abstract. Given aggregated mobile device data, the goal is to understand the impact of COVID-19 policy interventions on mobility. This problem is vital due to important societal use cases, such as safely reopening the economy. Challenges include understanding and interpreting questions of interest to policymakers, cross-jurisdictional variability in choice and time of interventions, the large data volume, and unknown sampling bias. The related work has explored the COVID-19 impact on travel distance, time spent at home, and the number of visitors at different points of interest. However, many policymakers are interested in long-duration visits to high-risk business categories and understanding the spatial selection bias to interpret summary reports. We provide an Entity Relationship diagram, system architecture, and implementation to support queries on long-duration visits in addition to fine resolution device count maps to understand spatial bias. We closely collaborated with policymakers to derive the system requirements and evaluate the system components, the summary reports, and visualizations. 

In systems engineering, verification activities evaluate the extent to which a system under development satisfies its requirements. In large systems engineering projects, multiple firms are involved in the system development, and hence verification activities must be coordinated. Self-interest impedes the implementation of verification strategies that are beneficial for all firms while encouraging each firm to choose a verification strategy beneficial to itself. Incentives for verification activities can motivate a single firm to adopt verification strategies beneficial to all firms in the project, but these incentives must be offered judiciously to minimize unnecessary expenditures and prevent the abuse of goodwill. In this paper, we use game theory to model a contractor-subcontractor scenario, in which the subcontractor provides a component to the contractor, who further integrates it into their system. Our model uses belief distributions to capture each firm’s epistemic uncertainty in their component’s state prior to verification, and we use multiscale decision theory to model interdependencies between the contractor and subcontractor’s design. We propose an incentive mechanism that aligns the verification strategies of the two firms and using our game-theoretic model, we identify those scenarios where the contractor benefits from incentivizing the subcontractor’s verification activities. 

Verification activities increase an engineering team’s confidence in its system design meeting system requirements, which in turn are derived from stakeholder needs. Conventional wisdom suggests that the system design should be verified frequently to minimize the cost of rework as the system design matures. However, this strategy is based more on experience of engineers than on a theoretical foundation. In this paper, we develop a belief-based model of verification of system design, using a single system requirement as an abstraction, to determine the conditions under which it is cost effective for an organization to verify frequently. We study the model for a broad set of growth rates in verification setup and rework costs. Our results show that verifying a system design frequently is not always an optimal verification strategy. Instead, it is only an optimal strategy when the costs of reworking a faulty design increase at a certain rate as the design matures.