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).

The COVID-19 pandemic has highlighted the need for quantitative modeling and analysis to understand real-world disease dynamics. In particular, post hoc analyses using compartmental models offer valuable insights into the effectiveness of public health interventions, such as vaccination strategies and containment policies. However, such compartmental models like SIR (Susceptible-Infectious-Recovered) often face limitations in directly incorporating noisy observational data. In this work, we employ Physics-Informed Neural Networks (PINNs) to solve the inverse problem of the SIR model using infection data from the Robert Koch Institute (RKI). Our main contribution is a fine-grained, spatio-temporal analysis of COVID-19 dynamics across all German federal states over a three-year period. We estimate state-specific transmission and recovery parameters and time-varying reproduction number (R_t) to track the pandemic progression. The results highlight strong variations in transmission behavior across regions, revealing correlations with vaccination uptake and temporal patterns associated with major pandemic phases. Our findings demonstrate the utility of PINNs in localized, long-term epidemiological modeling.

W in V, W is independent of V\ ( Descendants(W) Parents( W)) given Parents (W) . As expected we see that the number of detected causes by Granger is multiple times more than those of SyPI; in most cases Granger detects as causes all the candidate states. On the other hand, SyPI does not suffer from such problems even when there are latent confounders. Finally, in the third column, we report the detected distant causes. Strict thresholds (the default of SyPI method) are used for the analysis.

As large language models (LLMs) continue to evolve, questions about their trustworthiness in delivering factual information have become increasingly important. This concern also applies to their ability to accurately represent the geographic world. With recent advancements in this field, it is relevant to consider whether and to what extent LLMs' representations of the geographical world can be trusted. This study evaluates the performance of GPT-4o and Gemini 2.0 Flash in three key geospatial tasks: geocoding, elevation estimation, and reverse geocoding. In the geocoding task, both models exhibited systematic and random errors in estimating the coordinates of St. Anne's Column in Innsbruck, Austria, with GPT-4o showing greater deviations and Gemini 2.0 Flash demonstrating more precision but a significant systematic offset. For elevation estimation, both models tended to underestimate elevations across Austria, though they captured overall topographical trends, and Gemini 2.0 Flash performed better in eastern regions. The reverse geocoding task, which involved identifying Austrian federal states from coordinates, revealed that Gemini 2.0 Flash outperformed GPT-4o in overall accuracy and F1-scores, demonstrating better consistency across regions. Despite these findings, neither model achieved an accurate reconstruction of Austria's federal states, highlighting persistent misclassifications. The study concludes that while LLMs can approximate geographic information, their accuracy and reliability are inconsistent, underscoring the need for fine-tuning with geographical information to enhance their utility in GIScience and Geoinformatics.

"The Max Planck Society has created a scientific beacon of light here which beams far and wide, attracting both emerging and established scientists from all over the world," remarked Max Planck President Martin Stratmann. The new building, which houses all three of the Institute's departments, was constructed between September 2014 and March 2017. It was funded by the federal state of Baden-Württemberg's government which places great emphasis on research into intelligent systems: "With its Institute for Intelligent Systems in Tübingen and Stuttgart, the Max Planck Society has firmly established one of the key research fields in the digital transformation in Baden-Württemberg," indicated Minister-President Winfried Kretschmann. "The federal state has contributed € 41 million to the new building in Tübingen – this represents a sound investment which will help ensure that Baden-Württemberg remains a leading centre of research on artificial intelligence." The new building provides scientists with an outstanding environment in which to advance their theoretical and experimental research.