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We study various aspects of the first-order transduction quasi-order on graph classes, which provides a way of measuring the relative complexity of graph classes based on whether one can encode the other using a formula of first-order (FO) logic. In contrast with the conjectured simplicity of the transduction quasi-order for monadic second-order logic, the FO-transduction quasi-order is very complex, and many standard properties from structural graph theory and model theory naturally appear in it. We prove a local normal form for transductions among other general results and constructions, which we illustrate via several examples and via the characterizations of the transductions of some simple classes. We then turn to various aspects of the quasi-order, including the (non-)existence of minimum and maximum classes for certain properties, the strictness of the pathwidth hierarchy, the fact that the quasi-order is not a lattice, and the role of weakly sparse classes in the quasi-order.

Objective: This study introduces ChatSchema, an effective method for extracting and structuring information from unstructured data in medical paper reports using a combination of Large Multimodal Models (LMMs) and Optical Character Recognition (OCR) based on the schema. By integrating predefined schema, we intend to enable LMMs to directly extract and standardize information according to the schema specifications, facilitating further data entry. Method: Our approach involves a two-stage process, including classification and extraction for categorizing report scenarios and structuring information. We established and annotated a dataset to verify the effectiveness of ChatSchema, and evaluated key extraction using precision, recall, F1-score, and accuracy metrics. Based on key extraction, we further assessed value extraction. We conducted ablation studies on two LMMs to illustrate the improvement of structured information extraction with different input modals and methods. Result: We analyzed 100 medical reports from Peking University First Hospital and established a ground truth dataset with 2,945 key-value pairs. We evaluated ChatSchema using GPT-4o and Gemini 1.5 Pro and found a higher overall performance of GPT-4o. The results are as follows: For the result of key extraction, key-precision was 98.6%, key-recall was 98.5%, key-F1-score was 98.6%. For the result of value extraction based on correct key extraction, the overall accuracy was 97.2%, precision was 95.8%, recall was 95.8%, and F1-score was 95.8%. An ablation study demonstrated that ChatSchema achieved significantly higher overall accuracy and overall F1-score of key-value extraction, compared to the Baseline, with increases of 26.9% overall accuracy and 27.4% overall F1-score, respectively.

We study the construction and convergence of decoupling multistep schemes of higher order using the backward differentiation formulae for an elliptic-parabolic problem, which includes multiple-network poroelasticity as a special case. These schemes were first introduced in [Altmann, Maier, Unger, BIT Numer. Math., 64:20, 2024], where a convergence proof for the second-order case is presented. Here, we present a slightly modified version of these schemes using a different construction of related time delay systems. We present a novel convergence proof relying on concepts from G-stability applicable for any order and providing a sharper characterization of the required weak coupling condition. The key tool for the convergence analysis is the construction of a weighted norm enabling a telescoping argument for the sum of the errors.

Monitoring of hybrid systems attracts both scientific and practical attention. However, monitoring algorithms suffer from the methodological difficulty of only observing sampled discrete-time signals, while real behaviors are continuous-time signals. To mitigate this problem of sampling uncertainties, we introduce a model-bounded monitoring scheme, where we use prior knowledge about the target system to prune interpolation candidates. Technically, we express such prior knowledge by linear hybrid automata (LHAs) -- the LHAs are called bounding models. We introduce a novel notion of monitored language of LHAs, and we reduce the monitoring problem to the membership problem of the monitored language. We present two partial algorithms -- one is via reduction to reachability in LHAs and the other is a direct one using polyhedra -- and show that these methods, and thus the proposed model-bounded monitoring scheme, are efficient and practically relevant.

This study proposes a unified theory and statistical learning approach for traffic conflict detection, addressing the long-existing call for a consistent and comprehensive methodology to evaluate the collision risk emerging in road user interactions. The proposed theory assumes context-dependent probabilistic collision risk and frames conflict detection as assessing this risk by statistical learning of extreme events in daily interactions. Experiments using real-world trajectory data are conducted in this study, where a unified metric of conflict is trained with lane-changing interactions on German highways and applied to near-crash events from the 100-Car Naturalistic Driving Study in the U.S. Results of the experiments demonstrate that the trained metric provides effective collision warnings, generalises across distinct datasets and traffic environments, covers a broad range of conflicts, and delivers a long-tailed distribution of conflict intensity. Reflecting on these results, the unified theory ensures consistent evaluation by a generic formulation that encompasses varying assumptions of traffic conflicts; the statistical learning approach then enables a comprehensive consideration of influencing factors such as motion states of road users, environment conditions, and participant characteristics. Therefore, the theory and learning approach jointly provide an explainable and adaptable methodology for conflict detection among different road users and across various interaction scenarios. This promises to reduce accidents and improve overall traffic safety, by enhanced safety assessment of traffic infrastructures, more effective collision warning systems for autonomous driving, and a deeper understanding of road user behaviour in different traffic conditions.

Deep learning still struggles with certain kinds of scientific data. Notably, pretraining data may not provide coverage of relevant distribution shifts (e.g., shifts induced via the use of different measurement instruments). We consider deep learning models trained to classify the synthesis conditions of uranium ore concentrates (UOCs) and show that model editing is particularly effective for improving generalization to distribution shifts common in this domain. In particular, model editing outperforms finetuning on two curated datasets comprising of micrographs taken of U$_{3}$O$_{8}$ aged in humidity chambers and micrographs acquired with different scanning electron microscopes, respectively.

Spectral analysis of open surfaces is gaining momentum for studying surface morphology in engineering, computer graphics, and medical domains. This analysis is enabled using proper parameterization approaches on the target analysis domain. In this paper, we propose the usage of customizable parameterization coordinates that allow mapping open surfaces into oblate or prolate hemispheroidal surfaces. For this, we proposed the usage of Tutte, conformal, area-preserving, and balanced mappings for parameterizing any given simply connected open surface onto an optimal hemispheroid. The hemispheroidal harmonic bases were introduced to spectrally expand these parametric surfaces by generalizing the known hemispherical ones. This approach uses the radius of the hemispheroid as a degree of freedom to control the size of the parameterization domain of the open surfaces while providing numerically stable basis functions. Several open surfaces have been tested using different mapping combinations. We also propose optimization-based mappings to serve various applications on the reconstruction problem. Altogether, our work provides an effective way to represent and analyze simply connected open surfaces.

When applying reinforcement learning from human feedback (RLHF), the reward is learned from data and, therefore, always has some error. It is common to mitigate this by regularizing the policy with KL divergence from a base model, with the hope that balancing reward with regularization will achieve desirable outcomes despite this reward misspecification. We show that when the reward function has light-tailed error, optimal policies under less restrictive KL penalties achieve arbitrarily high utility. However, if error is heavy-tailed, some policies obtain arbitrarily high reward despite achieving no more utility than the base model--a phenomenon we call catastrophic Goodhart. We adapt a discrete optimization method to measure the tails of reward models, finding that they are consistent with light-tailed error. However, the pervasiveness of heavy-tailed distributions in many real-world applications indicates that future sources of RL reward could have heavy-tailed error, increasing the likelihood of reward hacking even with KL regularization.

Neuro-evolutionary methods have proven effective in addressing a wide range of tasks. However, the study of the robustness and generalizability of evolved artificial neural networks (ANNs) has remained limited. This has immense implications in the fields like robotics where such controllers are used in control tasks. Unexpected morphological or environmental changes during operation can risk failure if the ANN controllers are unable to handle these changes. This paper proposes an algorithm that aims to enhance the robustness and generalizability of the controllers. This is achieved by introducing morphological variations during the evolutionary training process. As a results, it is possible to discover generalist controllers that can handle a wide range of morphological variations sufficiently without the need of the information regarding their morphologies or adaptation of their parameters. We perform an extensive experimental analysis on simulation that demonstrates the trade-off between specialist and generalist controllers. The results show that generalists are able to control a range of morphological variations with a cost of underperforming on a specific morphology relative to a specialist. This research contributes to the field by addressing the limited understanding of robustness and generalizability and proposes a method by which to improve these properties.

We derive information-theoretic generalization bounds for supervised learning algorithms based on the information contained in predictions rather than in the output of the training algorithm. These bounds improve over the existing information-theoretic bounds, are applicable to a wider range of algorithms, and solve two key challenges: (a) they give meaningful results for deterministic algorithms and (b) they are significantly easier to estimate. We show experimentally that the proposed bounds closely follow the generalization gap in practical scenarios for deep learning.