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Graph neural networks are becoming increasingly popular in the field of machine learning due to their unique ability to process data structured in graphs. They have also been applied in safety-critical environments where perturbations inherently occur. However, these perturbations require us to formally verify neural networks before their deployment in safety-critical environments as neural networks are prone to adversarial attacks. While there exists research on the formal verification of neural networks, there is no work verifying the robustness of generic graph convolutional network architectures with uncertainty in the node features and in the graph structure over multiple message-passing steps. This work addresses this research gap by explicitly preserving the non-convex dependencies of all elements in the underlying computations through reachability analysis with (matrix) polynomial zonotopes. We demonstrate our approach on three popular benchmark datasets.

Double robustness (DR) is a widely-used property of estimators that provides protection against model misspecification and slow convergence of nuisance functions. While DR is a global property on the probability distribution manifold, it often coincides with influence curves, which only ensure orthogonality to nuisance directions locally. This apparent discrepancy raises fundamental questions about the theoretical underpinnings of DR. In this short communication, we address two key questions: (1) Why do influence curves frequently imply DR "for free"? (2) Under what conditions do DR estimators exist for a given statistical model and parameterization? Using tools from semiparametric theory, we show that convexity is the crucial property that enables influence curves to imply DR. We then derive necessary and sufficient conditions for the existence of DR estimators under a mean squared differentiable path-connected parameterization. Our main contribution also lies in the novel geometric interpretation of DR using information geometry. By leveraging concepts such as parallel transport, m-flatness, and m-curvature freeness, we characterize DR in terms of invariance along submanifolds. This geometric perspective deepens the understanding of when and why DR estimators exist. The results not only resolve apparent mysteries surrounding DR but also have practical implications for the construction and analysis of DR estimators. The geometric insights open up new connections and directions for future research. Our findings aim to solidify the theoretical foundations of a fundamental concept and contribute to the broader understanding of robust estimation in statistics.

We propose a constraint-based algorithm, which automatically determines causal relevance thresholds, to infer causal networks from data. We call these topological thresholds. We present two methods for determining the threshold: the first seeks a set of edges that leaves no disconnected nodes in the network; the second seeks a causal large connected component in the data. We tested these methods both for discrete synthetic and real data, and compared the results with those obtained for the PC algorithm, which we took as the benchmark. We show that this novel algorithm is generally faster and more accurate than the PC algorithm. The algorithm for determining the thresholds requires choosing a measure of causality. We tested our methods for Fisher Correlations, commonly used in PC algorithm (for instance in \cite{kalisch2005}), and further proposed a discrete and asymmetric measure of causality, that we called Net Influence, which provided very good results when inferring causal networks from discrete data. This metric allows for inferring directionality of the edges in the process of applying the thresholds, speeding up the inference of causal DAGs.

Extraction and synthesis of structured knowledge from extensive scientific literature are crucial for advancing and disseminating scientific progress. Although many existing systems facilitate literature review and digest, they struggle to process multimodal, varied, and inconsistent information within and across the literature into structured data. We introduce SciDaSynth, a novel interactive system powered by large language models (LLMs) that enables researchers to efficiently build structured knowledge bases from scientific literature at scale. The system automatically creates data tables to organize and summarize users' interested knowledge in literature via question-answering. Furthermore, it provides multi-level and multi-faceted exploration of the generated data tables, facilitating iterative validation, correction, and refinement. Our within-subjects study with researchers demonstrates the effectiveness and efficiency of SciDaSynth in constructing quality scientific knowledge bases. We further discuss the design implications for human-AI interaction tools for data extraction and structuring.

We propose a method to couple local and nonlocal diffusion models. By inheriting desirable properties such as patch tests, asymptotic compatibility and unintrusiveness from related splice and optimization-based coupling schemes, it enables the use of weak (or variational) formulations, is computationally efficient and straightforward to implement. We prove well-posedness of the coupling scheme and demonstrate its properties and effectiveness in a variety of numerical examples.

We investigate the computational power of particle methods, a well-established class of algorithms with applications in scientific computing and computer simulation. The computational power of a compute model determines the class of problems it can solve. Automata theory allows describing the computational power of abstract machines (automata) and the problems they can solve. At the top of the Chomsky hierarchy of formal languages and grammars are Turing machines, which resemble the concept on which most modern computers are built. Although particle methods can be interpreted as automata based on their formal definition, their computational power has so far not been studied. We address this by analyzing Turing completeness of particle methods. In particular, we prove two sets of restrictions under which a particle method is still Turing powerful, and we show when it loses Turing powerfulness. This contributes to understanding the theoretical foundations of particle methods and provides insight into the powerfulness of computer simulations.

The prevalence of digital media and evolving sociopolitical dynamics have significantly amplified the dissemination of hateful content. Existing studies mainly focus on classifying texts into binary categories, often overlooking the continuous spectrum of offensiveness and hatefulness inherent in the text. In this research, we present an extensive benchmark dataset for Amharic, comprising 8,258 tweets annotated for three distinct tasks: category classification, identification of hate targets, and rating offensiveness and hatefulness intensities. Our study highlights that a considerable majority of tweets belong to the less offensive and less hate intensity levels, underscoring the need for early interventions by stakeholders. The prevalence of ethnic and political hatred targets, with significant overlaps in our dataset, emphasizes the complex relationships within Ethiopia's sociopolitical landscape. We build classification and regression models and investigate the efficacy of models in handling these tasks. Our results reveal that hate and offensive speech can not be addressed by a simplistic binary classification, instead manifesting as variables across a continuous range of values. The Afro-XLMR-large model exhibits the best performances achieving F1-scores of 75.30%, 70.59%, and 29.42% for the category, target, and regression tasks, respectively. The 80.22% correlation coefficient of the Afro-XLMR-large model indicates strong alignments.

This study introduces a new approach to optimize the geometrical parameters of pipe diffusers in centrifugal compressors for Micro Gas Turbines, tailored for a 100 kW unit. The methodology draws insights from optimized airfoil-type diffusers and addresses the unique topological challenges of pipe diffusers, using diffuser maps to enhance design precision. The effectiveness of this method is validated through 3D-RANS based steady CFD simulations, using the ANSYS CFX solver. Comparative performance assessments at 100 percent rotation speed show that the best-performing pipe diffuser slightly trails its airfoil counterpart in efficiency, achieving 82.2 percent total-to-total isentropic efficiency compared to 84.4 percent. However, it offers a reduced frontal area, enhancing compactness. The analysis also reveals a dualistic impact from the leading-edge geometry of the pipe diffuser, which generates two counter-rotating vortices. These vortices have beneficial effects in pseudo and semi-vaneless spaces while introducing destabilizing factors in channel spaces. This investigation highlights potential trade-offs and outlines conditions under which adverse effects dominate, leading to significant flow separation. These insights pave the way for refining diffuser designs to better balance performance with spatial efficiency, marking a critical step forward in compressor technology of micro gas turbine for decentralized power systems.

We introduce the optimized dynamic mode decomposition algorithm for constructing an adaptive and computationally efficient reduced order model and forecasting tool for global atmospheric chemistry dynamics. By exploiting a low-dimensional set of global spatio-temporal modes, interpretable characterizations of the underlying spatial and temporal scales can be computed. Forecasting is also achieved with a linear model that uses a linear superposition of the dominant spatio-temporal features. The DMD method is demonstrated on three months of global chemistry dynamics data, showing its significant performance in computational speed and interpretability. We show that the presented decomposition method successfully extracts known major features of atmospheric chemistry, such as summertime surface pollution and biomass burning activities. Moreover, the DMD algorithm allows for rapid reconstruction of the underlying linear model, which can then easily accommodate non-stationary data and changes in the dynamics.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.