Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation. In this work, we present a formal analysis of the quotient geometry underlying the TTN parameter space. Our framework allows for arbitrary horizontal distributions, and we develop efficient first- and second-order optimization algorithms that exploit this geometry. Additionally, we devise a backpropagation algorithm for training TTNs in a kernel learning setting. We validate our methods through numerical experiments on a representative digit classification task and reveal an important tradeoff between two different horizontal distributions that are available for TTNs: while one offers cleaner geometric statements, the other ultimately leads to more efficient algorithms.
The global expansion of renewable electricity production implies an increasing need for flexibility options. Currently, the construction of Battery Electricity Storage Systems (BESS) is booming. In Europe, Continuous Intraday Markets (CID) pose an important platform for short-term balancing of stochastic demand and intermittent production. This paper studies the stochastic decision problem of optimal BESS operation in CID-markets for maximal profit under future price uncertainty. Using dynamic programming, we mathematically formulate an optimal solution and derive major properties, which allow to present a numerically feasible algorithm for CID-trading with batteries. Supposing market efficiency and a Markovian model, we apply this algorithm to the German market in a backtesting simulation study for the years 2022 to 2025. On average, we generate an annual cash flow between 30,678 EUR and 56,016 EUR per 1 MWh of usable capacity, depending on technical conditions of the battery (C-rate, efficiency, usage intensity). These revenues are stable within the considered horizon apart from yearly seasonality and make up 82% of a benchmark with perfect-foresight under realistic technical conditions.
The use of conventional plastic mulch films is a common agricultural practice that can lead to persistent plastic film fragments entering soil systems. To prevent the accumulation of these fragments, soil-biodegradable mulch films are marketed as alternatives. Unlike conventional plastic mulch, soil-biodegradable mulch films are ploughed into the soil after use, where they biodegrade over time. This study aims to elucidate the effects of soil-biodegradable mulch film fragments—following six months of application on the soil surface—ploughed into soil on surface runoff, soil erosion, and lateral mulch film fragment loss during simulated rainfall events. Our results showed a significant increase in runoff coefficient for the pre-wetted (wet run) simulations in soils with soil-biodegradable mulch film fragments compared to soils without them, while differences in sediment delivery were insignificant. In the delivered sediments, large mulch film fragments (> 2 mm) were depleted, whereas small fragments (< 2 mm) were transported approximately proportionally to the topsoil of the plots. Overall, our results indicate that film fragments can affect surface runoff on arable land, and generally, soil erosion is a pathway of soil-biodegradable mulch film fragments transport into adjacent ecosystems, which is especially effective in the case of small film fragments (< 2 mm) available from topsoil.
Background The Interactive-Constructive-Active-Passive (ICAP) framework makes assumptions about the relationships between observable types of learning activities (passive, active, constructive, interactive), cognitive processes, and learning outcomes. Yet, rigorous empirical studies are still lacking establishing the validity of the ICAP framework. Aims This study investigates the effects of student engagement in passive, active, constructive and interactive learning activities on their surface and deep knowledge gain, and their motivation. Additionally, the study aims to determine the associations between students’ cognitive processes, their learning activities, as well as surface and deep knowledge gain. Sample Participants were 249 pre-service teachers. Methods After reading a text on multimedia learning, participants were asked to reread the text (passive condition), to underline central information in the text (active condition), to work on three open-ended tasks addressing the text (constructive condition), or to work on the same tasks in pairs (interactive condition). Results No statistically significant effects of condition on surface or deep knowledge could be detected. Regarding motivation, participants in the interactive condition reported statistically significantly higher levels of perceived relatedness compared to all other conditions. Furthermore, only participants in the interactive condition reported statistically significantly higher levels of interactive cognitive processes compared to those in all other conditions. Constructive cognitive processes were statistically significantly negatively associated with deep knowledge gain. Conclusion The findings suggest that the empirical foundation supporting the ICAP framework may not yet be sufficiently robust. Yet, more research is needed that applies a more rigorous methodology exploring the ICAP framework.
Negative electricity prices have become increasingly frequent across European power markets in recent years, raising critical challenges for market participants, policymakers, and researchers. While much of the existing empirical literature has focused on Germany, where negative prices first appeared in 2008, this study systematically analyzes and compares their drivers across 20 European electricity markets. Using hourly data for the period 2015–2024, we employ both country-specific and panel logistic regression models to identify the fundamental determinants of negative price events. The results reveal broad commonalities across markets, complemented by notable country-specific deviations. Negative prices exhibit strong persistence and pronounced seasonal patterns, while higher electricity demand systematically reduces their likelihood. The generation mix proves decisive: higher combined wind and solar generation is positively associated with the probability of negative price, whereas the effects of other renewables (e.g., biomass, geothermal, hydro) vary by country. By contrast, non-renewable generation is generally associated with a lower probability of negative prices, although the strength of this relationship varies across countries, while the role of cross-border electricity flows remains heterogeneous and context-dependent.
