Figure5: Detectedcausal pathsof the spreadof Covid-19amongthe federalGermanstates, including causes among the restriction measures taken by each federal state. Each colour (in arrows and policies) indicates causes of one state (see top legend). The four subfigures correspond to the four combinations of threshold 1 and 2 that we tested. A distribution P is faithful to a directed acyclic graph (DAG) G if no conditionalindependence relationsotherthanthe onesentailed by the Markov property are present. Let G be a causal graph with vertex setV and P be a probability distribution over the vertices inV generated by the causal structure represented by G. G and P satisfy the Causal Markov Condition if and only if for every W in V, W is independent of V\(Descendants(W) Parents(W)) given Parents(W).

We resolve a 30-year-old open problem concerning the power of unlabeled data in online learning by tightly quantifying the gap between transductive and standard online learning. In the standard setting, the optimal mistake bound is characterized by the Littlestone dimension $d$ of the concept class $H$ (Littlestone 1987). We prove that in the transductive setting, the mistake bound is at least $Ω(\sqrt{d})$. This constitutes an exponential improvement over previous lower bounds of $Ω(\log\log d)$, $Ω(\sqrt{\log d})$, and $Ω(\log d)$, due respectively to Ben-David, Kushilevitz, and Mansour (1995, 1997) and Hanneke, Moran, and Shafer (2023). We also show that this lower bound is tight: for every $d$, there exists a class of Littlestone dimension $d$ with transductive mistake bound $O(\sqrt{d})$. Our upper bound also improves upon the best known upper bound of $(2/3)d$ from Ben-David, Kushilevitz, and Mansour (1997). These results establish a quadratic gap between transductive and standard online learning, thereby highlighting the benefit of advance access to the unlabeled instance sequence. This contrasts with the PAC setting, where transductive and standard learning exhibit similar sample complexities.

While optimization-based methods boast gen-eralizability across modalities and robust performance, learning-based methods promise peak performance, incorporating weak supervision and amortized optimization. However, the exact conditions for either paradigm to perform well over the other are shrouded and not explicitly outlined in the existing literature.

Danish PM calls for strong answer from EU leaders to Russia's hybrid attacks EU leaders have met in Copenhagen under pressure to boost European defence after a series of Russian incursions into EU airspace, and days after drones targeted Danish airports. Danish Prime Minister Mette Frederiksen told reporters that from a European perspective there is only one country... willing to threaten us and that is Russia, and therefore we need a very strong answer back. The incursions have become most acute for countries on the EU's eastern flank such as Poland and Estonia. A number of member states have already backed plans for a multi-layered drone wall to quickly detect, then track and destroy Russian drones. We meet at a time when Russia have intensified their attacks in Ukraine, where we have seen Russian airspace violations and unwanted drone activity in several European countries, Frederiksen told a news conference after the talks had concluded.

Can Ukraine restore its pre-war borders? Is Russia testing NATO with aerial incursions in Europe? Poland has briefly closed part of its airspace southeast of capital Warsaw, citing "unplanned military activity", as Russia launches a new wave of strikes against Ukraine. The deployment on Sunday of Polish and allied aircraft in the country's airspace comes as the transatlantic security bloc NATO announced that it is upgrading its mission in the Baltic Sea in response to drone incursions in Denmark and reported drone sightings in Norway. In the latest incident, the Polish armed forces said it scrambled aircraft to ensure the security of its airspace after Russia launched strikes on Ukraine.

In particular, it holds for classical QGT. Although dispersion has been used before in GT, c.f., [ The last fact explains why further increase of is not needed.

Large language models (LLMs) are now widely accessible, reaching learners at all educational levels. This development has raised concerns that their use may circumvent essential learning processes and compromise the integrity of established assessment formats. In physics education, where problem solving plays a central role in instruction and assessment, it is therefore essential to understand the physics-specific problem-solving capabilities of LLMs. Such understanding is key to informing responsible and pedagogically sound approaches to integrating LLMs into instruction and assessment. This study therefore compares the problem-solving performance of a general-purpose LLM (GPT-4o, using varying prompting techniques) and a reasoning-optimized model (o1-preview) with that of participants of the German Physics Olympiad, based on a set of well-defined Olympiad problems. In addition to evaluating the correctness of the generated solutions, the study analyzes characteristic strengths and limitations of LLM-generated solutions. The findings of this study indicate that both tested LLMs (GPT-4o and o1-preview) demonstrate advanced problem-solving capabilities on Olympiad-type physics problems, on average outperforming the human participants. Prompting techniques had little effect on GPT-4o's performance, while o1-preview almost consistently outperformed both GPT-4o and the human benchmark. Based on these findings, the study discusses implications for the design of summative and formative assessment in physics education, including how to uphold assessment integrity and support students in critically engaging with LLMs.

Accurate epidemic forecasting is crucial for effective disease control and prevention. Traditional compartmental models often struggle to estimate temporally and spatially varying epidemiological parameters, while deep learning models typically overlook disease transmission dynamics and lack interpretability in the epidemiological context. To address these limitations, we propose a novel Causal Spatiotemporal Graph Neural Network (CSTGNN), a hybrid framework that integrates a Spatio-Contact SIR model with Graph Neural Networks (GNNs) to capture the spatiotemporal propagation of epidemics. Inter-regional human mobility exhibits continuous and smooth spatiotemporal patterns, leading to adjacent graph structures that share underlying mobility dynamics. To model these dynamics, we employ an adaptive static connectivity graph to represent the stable components of human mobility and utilize a temporal dynamics model to capture fluctuations within these patterns. By integrating the adaptive static connectivity graph with the temporal dynamics graph, we construct a dynamic graph that encapsulates the comprehensive properties of human mobility networks. Additionally, to capture temporal trends and variations in infectious disease spread, we introduce a temporal decomposition model to handle temporal dependence. This model is then integrated with a dynamic graph convolutional network for epidemic forecasting. We validate our model using real-world datasets at the provincial level in China and the state level in Germany. Extensive studies demonstrate that our method effectively models the spatiotemporal dynamics of infectious diseases, providing a valuable tool for forecasting and intervention strategies. Furthermore, analysis of the learned parameters offers insights into disease transmission mechanisms, enhancing the interpretability and practical applicability of our model.