Observational studies are an important tool for determining whether the findings from controlled experiments can be transferred into scenarios that are closer to subjects' real-life circumstances. A rigorous approach to observational studies involves collecting data from different sensors to comprehensively capture the situation of the subject. However, this leads to technical difficulties especially if the sensors are from different manufacturers, as multiple data collection tools have to run simultaneously. We present SensorHub, a system that can collect data from various wearable devices from different manufacturers, such as inertial measurement units, portable electrocardiographs, portable electroencephalographs, portable photoplethysmographs, and sensors for electrodermal activity. Additionally, our tool offers the possibility to include ecological momentary assessments (EMAs) in studies. Hence, SensorHub enables multimodal sensor data collection under real-world conditions and allows direct user feedback to be collected through questionnaires, enabling studies at home. In a first study with 11 participants, we successfully used SensorHub to record multiple signals with different devices and collected additional information with the help of EMAs. In addition, we evaluated SensorHub's technical capabilities in several trials with up to 21 participants recording simultaneously using multiple sensors with sampling frequencies as high as 1000 Hz. We could show that although there is a theoretical limitation to the transmissible data rate, in practice this limitation is not an issue and data loss is rare. We conclude that with modern communication protocols and with the increasingly powerful smartphones and wearables, a system like our SensorHub establishes an interoperability framework to adequately combine consumer-grade sensing hardware which enables observational studies in real life.

According to Radzikowski’s celebrated results, bisolutions of a wave operator on a globally hyperbolic spacetime are of the Hadamard form iff they are given by a linear combination of distinguished parametrices i2(G˜aF−G˜F+G˜A−G˜R) in the sense of Duistermaat and Hörmander [Acta Math. 128, 183–269 (1972)] and Radzikowski [Commun. Math. Phys. 179, 529 (1996)]. Inspired by the construction of the corresponding advanced and retarded Green operator GA, GR as done by Bär, Ginoux, and Pfäffle {Wave Equations on Lorentzian Manifolds and Quantization [European Mathematical Society (EMS), Zürich, 2007]}, we construct the remaining two Green operators GF, GaF locally in terms of Hadamard series. Afterward, we provide the global construction of i2(G˜aF−G˜F), which relies on new techniques such as a well-posed Cauchy problem for bisolutions and a patching argument using Čech cohomology. This leads to global bisolutions of the Hadamard form, each of which can be chosen to be a Hadamard two-point-function, i.e., the smooth part can be adapted such that, additionally, the symmetry and the positivity condition are exactly satisfied.

River-valley morphology preserves information on tectonic and climatic conditions that shape landscapes. Observations suggest that river discharge and valley-wall lithology are the main controls on valley width. Yet, current models based on these observations fail to explain the full range of cross-sectional valley shapes in nature, suggesting hitherto unquantified controls on valley width. In particular, current models cannot explain the existence of paired terrace sequences that form under cyclic climate forcing. Paired river terraces are staircases of abandoned floodplains on both valley sides, and hence preserve past valley widths. Their formation requires alternating phases of predominantly river incision and predominantly lateral planation, plus progressive valley narrowing. While cyclic Quaternary climate changes can explain shifts between incision and lateral erosion, the driving mechanism of valley narrowing is unknown. Here, we extract valley geometries from climatically formed, alluvial river-terrace sequences and show that across our dataset, the total cumulative terrace height (here: total valley height) explains 90%–99% of the variance in valley width at the terrace sites. This finding suggests that valley height, or a parameter that scales linearly with valley height, controls valley width in addition to river discharge and lithology. To explain this valley-width-height relationship, we reformulate existing valley-width models and suggest that, when adjusting to new boundary conditions, alluvial valleys evolve to a width at which sediment removal from valley walls matches lateral sediment supply from hillslope erosion. Such a hillslope-channel coupling is not captured in current valley-evolution models. Our model can explain the existence of paired terrace sequences under cyclic climate forcing and relates valley width to measurable field parameters. Therefore, it facilitates the reconstruction of past climatic and tectonic conditions from valley topography.

Dynamic pricing is considered a possibility to gain an advantage over competitors in modern online markets. The past advancements in Reinforcement Learning (RL) provided more capable algorithms that can be used to solve pricing problems. In this paper, we study the performance of Deep Q-Networks (DQN) and Soft Actor Critic (SAC) in different market models. We consider tractable duopoly settings, where optimal solutions derived by dynamic programming techniques can be used for verification, as well as oligopoly settings, which are usually intractable due to the curse of dimensionality. We find that both algorithms provide reasonable results, while SAC performs better than DQN. Moreover, we show that under certain conditions, RL algorithms can be forced into collusion by their competitors without direct communication.