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We analyse efficient risk-sharing arrangements when the value from deviating is determined endogenously by another risk-sharing arrangement. Coalitions form to insure against idiosyncratic income risk. Self-enforcing contracts for both the original coalition and any coalition formed (joined) after deviations rely on a belief in future cooperation which we term “trust”. We treat the contracting conditions of original and deviation coalitions symmetrically and show that higher trust tightens incentive constraints since it facilitates the formation of deviating coalitions. As a consequence, although trust facilitates the initial formation of coalitions, the extent of risk sharing in successfully formed coalitions is declining in the extent of trust and efficient allocations might feature resource burning or utility burning: trust is indeed a double-edged sword.

 

We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of 85.69- and 99.02-GHz continuum emission and H42α and H40α lines emission from the central 1 kpc of NGC 1808. These forms of emission are tracers of photoionizing stars but unaffected by dust obscuration that we use to test the applicability of other commonly star formation metrics. An analysis of the spectral energy distributions shows that free–free emission contributes about 60–90 per cent of the continuum emission in the 85–100-GHz frequency range, dependent on the region. The star formation rate (SFR) derived from the ALMA free–free emission is 3.1 ± 0.3 M⊙ yr−1. This is comparable to the SFRs measured from the infrared emission, mainly because most of the bolometric energy from the heavily obscured region is emitted as infrared emission. The radio 1.5-GHz emission yields an SFR 25 per cent lower than the ALMA value, probably because of the diffusion of the electrons producing the synchrotron emission beyond the star-forming regions. The SFRs measured from the extinction-corrected H α line emission are about 40–65 per cent of the SFR derived from the ALMA data, likely because this metric was not calibrated for high-extinction regions. Some SFRs based on extinction-corrected ultraviolet emission are similar to those from ALMA and infrared data, but given that the ultraviolet terms in the extinction correction equations are very small, these metrics seem inappropriate to apply to this dusty starburst.

 

The wide availability of data coupled with the computational advances in artificial intelligence and machine learning promise to enable many future technologies such as autonomous driving. While there has been a variety of successful demonstrations of these technologies, critical system failures have repeatedly been reported. Even if rare, such system failures pose a serious barrier to adoption without a rigorous risk assessment. This article presents a framework for the systematic and rigorous risk verification of systems. We consider a wide range of system specifications formulated in signal temporal logic (STL) and model the system as a stochastic process, permitting discrete-time and continuous-time stochastic processes. We then define the STL robustness risk as the risk of lacking robustness against failure . This definition is motivated as system failures are often caused by missing robustness to modeling errors, system disturbances, and distribution shifts in the underlying data generating process. Within the definition, we permit general classes of risk measures and focus on tail risk measures such as the value-at-risk and the conditional value-at-risk. While the STL robustness risk is in general hard to compute, we propose the approximate STL robustness risk as a more tractable notion that upper bounds the STL robustness risk. We show how the approximate STL robustness risk can accurately be estimated from system trajectory data. For discrete-time stochastic processes, we show under which conditions the approximate STL robustness risk can even be computed exactly. We illustrate our verification algorithm in the autonomous driving simulator CARLA and show how a least risky controller can be selected among four neural network lane-keeping controllers for five meaningful system specifications. 

Abstract Magnetic transition metal chalcogenides form an emerging platform for exploring spin-orbit driven Berry phase phenomena owing to the nontrivial interplay between topology and magnetism. Here we show that the anomalous Hall effect in pristine Cr 2 Te 3 thin films manifests a unique temperature-dependent sign reversal at nonzero magnetization, resulting from the momentum-space Berry curvature as established by first-principles simulations. The sign change is strain tunable, enabled by the sharp and well-defined substrate/film interface in the quasi-two-dimensional Cr 2 Te 3 epitaxial films, revealed by scanning transmission electron microscopy and depth-sensitive polarized neutron reflectometry. This Berry phase effect further introduces hump-shaped Hall peaks in pristine Cr 2 Te 3 near the coercive field during the magnetization switching process, owing to the presence of strain-modulated magnetic layers/domains. The versatile interface tunability of Berry curvature in Cr 2 Te 3 thin films offers new opportunities for topological electronics.