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Generalization problems in languages with binders involve computing the most common structure between expressions while respecting bound variable renaming and freshness constraints. These problems often lack a least general solution. However, leveraging nominal techniques, we previously demonstrated that a semantic approach with atom-variables enables the elimination of redundant solutions and allows for computing unique least general generalizations (LGGs). In this work, we extend this approach to handle associative (A), commutative (C), and associative-commutative (AC) equational theories. We present a sound and weak complete algorithm for solving equational generalization problems, which generates finite weak minimal complete sets of LGGs for each theory. A key challenge arises from solving equivariance problems while taking into account these equational theories, as identifying redundant generalizations requires recognizing when one expression (with binders) is a renaming of another while possibly considering permutations of sub-expressions. This unexpected interaction between renaming and equational reasoning made this particularly difficult, necessitating semantic tests within the equivariance algorithm. Given that these equational theories naturally induce exponentially large LGG sets due to subexpression permutations, future work could explore restricted theory fragments where the generalization problem remains unitary. In these fragments, LGGs can be computed efficiently in polynomial time, offering practical benefits for symbolic computation and automated reasoning tasks.

Multi-class segmentation of the aorta in computed tomography angiography (CTA) scans is essential for diagnosing and planning complex endovascular treatments for patients with aortic dissections. However, existing methods reduce aortic segmentation to a binary problem, limiting their ability to measure diameters across different branches and zones. Furthermore, no open-source dataset is currently available to support the development of multi-class aortic segmentation methods. To address this gap, we organized the AortaSeg24 MICCAI Challenge, introducing the first dataset of 100 CTA volumes annotated for 23 clinically relevant aortic branches and zones. This dataset was designed to facilitate both model development and validation. The challenge attracted 121 teams worldwide, with participants leveraging state-of-the-art frameworks such as nnU-Net and exploring novel techniques, including cascaded models, data augmentation strategies, and custom loss functions. We evaluated the submitted algorithms using the Dice Similarity Coefficient (DSC) and Normalized Surface Distance (NSD), highlighting the approaches adopted by the top five performing teams. This paper presents the challenge design, dataset details, evaluation metrics, and an in-depth analysis of the top-performing algorithms. The annotated dataset, evaluation code, and implementations of the leading methods are publicly available to support further research. All resources can be accessed at https://aortaseg24.grand-challenge.org.

Breast cancer is one of the most common causes of death among women worldwide. Early detection helps in reducing the number of deaths. Automated 3D Breast Ultrasound (ABUS) is a newer approach for breast screening, which has many advantages over handheld mammography such as safety, speed, and higher detection rate of breast cancer. Tumor detection, segmentation, and classification are key components in the analysis of medical images, especially challenging in the context of 3D ABUS due to the significant variability in tumor size and shape, unclear tumor boundaries, and a low signal-to-noise ratio. The lack of publicly accessible, well-labeled ABUS datasets further hinders the advancement of systems for breast tumor analysis. Addressing this gap, we have organized the inaugural Tumor Detection, Segmentation, and Classification Challenge on Automated 3D Breast Ultrasound 2023 (TDSC-ABUS2023). This initiative aims to spearhead research in this field and create a definitive benchmark for tasks associated with 3D ABUS image analysis. In this paper, we summarize the top-performing algorithms from the challenge and provide critical analysis for ABUS image examination. We offer the TDSC-ABUS challenge as an open-access platform at https://tdsc-abus2023.grand-challenge.org/ to benchmark and inspire future developments in algorithmic research.

Multiple Instance Learning (MIL) methods allow for gigapixel Whole-Slide Image (WSI) analysis with only slide-level annotations. Interpretability is crucial for safely deploying such algorithms in high-stakes medical domains. Traditional MIL methods offer explanations by highlighting salient regions. However, such spatial heatmaps provide limited insights for end users. To address this, we propose a novel inherently interpretable WSI-classification approach that uses human-understandable pathology concepts to generate explanations. Our proposed Concept MIL model leverages recent advances in vision-language models to directly predict pathology concepts based on image features. The model's predictions are obtained through a linear combination of the concepts identified on the top-K patches of a WSI, enabling inherent explanations by tracing each concept's influence on the prediction. In contrast to traditional concept-based interpretable models, our approach eliminates the need for costly human annotations by leveraging the vision-language model. We validate our method on two widely used pathology datasets: Camelyon16 and PANDA. On both datasets, Concept MIL achieves AUC and accuracy scores over 0.9, putting it on par with state-of-the-art models. We further find that 87.1\% (Camelyon16) and 85.3\% (PANDA) of the top 20 patches fall within the tumor region. A user study shows that the concepts identified by our model align with the concepts used by pathologists, making it a promising strategy for human-interpretable WSI classification.

Digital pathology offers a groundbreaking opportunity to transform clinical practice in histopathological image analysis, yet faces a significant hurdle: the substantial file sizes of pathological Whole Slide Images (WSI). While current digital pathology solutions rely on lossy JPEG compression to address this issue, lossy compression can introduce color and texture disparities, potentially impacting clinical decision-making. While prior research addresses perceptual image quality and downstream performance independently of each other, we jointly evaluate compression schemes for perceptual and downstream task quality on four different datasets. In addition, we collect an initially uncompressed dataset for an unbiased perceptual evaluation of compression schemes. Our results show that deep learning models fine-tuned for perceptual quality outperform conventional compression schemes like JPEG-XL or WebP for further compression of WSI. However, they exhibit a significant bias towards the compression artifacts present in the training data and struggle to generalize across various compression schemes. We introduce a novel evaluation metric based on feature similarity between original files and compressed files that aligns very well with the actual downstream performance on the compressed WSI. Our metric allows for a general and standardized evaluation of lossy compression schemes and mitigates the requirement to independently assess different downstream tasks. Our study provides novel insights for the assessment of lossy compression schemes for WSI and encourages a unified evaluation of lossy compression schemes to accelerate the clinical uptake of digital pathology.

The Sachdev-Ye-Kitaev (SYK) model is a paradigm for extreme quantum chaos, non-Fermi-liquid behavior, and holographic matter. Yet, the dense random all-to-all interactions that characterize it are an extreme challenge for realistic laboratory realizations. Here, we propose a general scheme for densifying the coupling distribution of random disorder Hamiltonians, using a Trotterized cycling through sparse time-dependent disorder realizations. To diagnose the convergence of sparse to dense models, we introduce an information-theory inspired diagnostic. We illustrate how the scheme can come to bear in the realization of the complex SYK$_4$ model in cQED platforms with available experimental resources, using a single cavity mode together with a fast cycling through independent speckle patterns. The simulation scheme applies to the SYK class of models as well as spin glasses, spin liquids, and related disorder models, bringing them into reach of quantum simulation using single-mode cavity-QED setups and other platforms., Comment: the first two authors contributed equally to this work

The X-ray polarization observations made possible with the Imaging X-ray Polarimetry Explorer (IXPE) offer new ways of probing high-energy emission processes in astrophysical jets from blazars. Here we report on the first X-ray polarization observation of the blazar S4 0954+65 in a high optical and X-ray state. During our multi-wavelength campaign on the source, we detected an optical flare whose peak coincided with the peak of an X-ray flare. This optical-X-ray flare most likely took place in a feature moving along the parsec-scale jet, imaged at 43 GHz by the Very Long Baseline Array. The 43 GHz polarization angle of the moving component underwent a rotation near the time of the flare. In the optical band, prior to the IXPE observation, we measured the polarization angle to be aligned with the jet axis. In contrast, during the optical flare the optical polarization angle was perpendicular to the jet axis; after the flare, it reverted to being parallel to the jet axis. Due to the smooth behavior of the optical polarization angle during the flare, we favor shocks as the main acceleration mechanism. We also infer that the ambient magnetic field lines in the jet were parallel to the jet position angle. The average degree of optical polarization during the IXPE observation was (14.3$\pm$4.1)%. Despite the flare, we only detected an upper limit of 14% (at 3$\sigma$ level) on the X-ray polarization degree; although a reasonable assumption on the X-ray polarization angle results in an upper limit of 8.8% ($3\sigma$). We model the spectral energy distribution (SED) and spectral polarization distribution (SPD) of S4 0954+65 with leptonic (synchrotron self-Compton) and hadronic (proton and pair synchrotron) models. The constraints we obtain with our combined multi-wavelength polarization observations and SED modeling tentatively disfavor hadronic models for the X-ray emission in S4 0954+65., Comment: Submitted to A&A, 16 pages, 5 figures, and 7 tables

How can we test AI performance? This question seems trivial, but it isn't. Standard benchmarks often have problems such as in-distribution and small-size test sets, oversimplified metrics, unfair comparisons, and short-term outcome pressure. As a consequence, good performance on standard benchmarks does not guarantee success in real-world scenarios. To address these problems, we present Touchstone, a large-scale collaborative segmentation benchmark of 9 types of abdominal organs. This benchmark is based on 5,195 training CT scans from 76 hospitals around the world and 5,903 testing CT scans from 11 additional hospitals. This diverse test set enhances the statistical significance of benchmark results and rigorously evaluates AI algorithms across various out-of-distribution scenarios. We invited 14 inventors of 19 AI algorithms to train their algorithms, while our team, as a third party, independently evaluated these algorithms on three test sets. In addition, we also evaluated pre-existing AI frameworks--which, differing from algorithms, are more flexible and can support different algorithms--including MONAI from NVIDIA, nnU-Net from DKFZ, and numerous other open-source frameworks. We are committed to expanding this benchmark to encourage more innovation of AI algorithms for the medical domain., Comment: Accepted to NeurIPS-2024

What representation do deep neural networks learn? How similar are images to each other for neural networks? Despite the overwhelming success of deep learning methods key questions about their internal workings still remain largely unanswered, due to their internal high dimensionality and complexity. To address this, one approach is to measure the similarity of activation responses to various inputs. Representational Similarity Matrices (RSMs) distill this similarity into scalar values for each input pair. These matrices encapsulate the entire similarity structure of a system, indicating which input leads to similar responses. While the similarity between images is ambiguous, we argue that the spatial location of semantic objects does neither influence human perception nor deep learning classifiers. Thus this should be reflected in the definition of similarity between image responses for computer vision systems. Revisiting the established similarity calculations for RSMs we expose their sensitivity to spatial alignment. In this paper, we propose to solve this through semantic RSMs, which are invariant to spatial permutation. We measure semantic similarity between input responses by formulating it as a set-matching problem. Further, we quantify the superiority of semantic RSMs over spatio-semantic RSMs through image retrieval and by comparing the similarity between representations to the similarity between predicted class probabilities., Comment: Accepted at NeurIPS2024

This extended abstract describes the challenges in implementing recommender systems for digital archives in the humanities, focusing on Monasterium.net, a platform for historical legal documents. We discuss three key aspects: (i) the unique characteristics of so-called charters as items for recommendation, (ii) the complex multi-stakeholder environment, and (iii) the distinct information-seeking behavior of scholars in the humanities. By examining these factors, we aim to contribute to the development of more effective and tailored recommender systems for (digital) humanities research., Comment: Presented at AltRecSys 2024: The First Workshop on Alternative, Unexpected, and Critical Ideas in Recommendation, October 18, 2024, co-located with the ACM Conference on Recommender Systems 2024 (RecSys 2024), Bari, Italy

Synchrotron X-ray emission has been detected from nearly a dozen young supernova remnants (SNRs). X-rays of synchrotron origin exhibit linear polarization in a regular, non-randomly oriented magnetic field. The significant polarized X-ray emission from four such SNRs has already been reported on the basis of observations with the Imaging X-ray Polarimetry Explorer (IXPE). The magnetic-field structure as derived from IXPE observations is radial for Cassiopeia A, Tycho's SNR, and SN 1006, and tangential for RX J1713.7-3946. The latter together with the recent detection of a tangential magnetic field in SNR 1E 0102.2-7219 by the Australia Telescope Compact Array in the radio band shows that tangential magnetic fields can also be present in young SNRs. Thus, the dichotomy in polarization between young and middle-aged SNRs (radial magnetic fields in young SNRs, but tangential magnetic fields in middle-aged SNRs), previously noticed in the radio band, deserves additional attention. The present analysis of IXPE observations determines, for the first time, a magnetic-field structure in the northwestern rim of Vela Jr, also known as RX J0852.0-4622, and provides a new example of a young SNR with a tangential magnetic field., Comment: Accepted for publication in Astronomy and Astrophysics

X-ray polarization is a unique new probe of the particle acceleration in astrophysical jets made possible through the Imaging X-ray Polarimetry Explorer. Here we report on the first dense X-ray polarization monitoring campaign on the blazar Mrk 421. Our observations were accompanied by an even denser radio and optical polarization campaign. We find significant short-timescale variability in both X-ray polarization degree and angle, including a $\sim90^\circ$ angle rotation about the jet axis. We attribute this to random variations of the magnetic field, consistent with the presence of turbulence but also unlikely to be explained by turbulence alone. At the same time, the degree of lower-energy polarization is significantly lower and shows no more than mild variability. Our campaign provides further evidence for a scenario in which energy-stratified shock-acceleration of relativistic electrons, combined with a turbulent magnetic field, is responsible for optical to X-ray synchrotron emission in blazar jets., Comment: 23 pages, including 8 pages of appendices. 12 figures, 3 tables. Submitted to ApJ

Following limb amputation, neural signals for limb functions persist in the residual peripheral nerves. Targeted muscle reinnervation (TMR) allows to redirected these signals into spare muscles to recover the neural information through electromyography (EMG). However, a significant challenge arises in separating distinct neural commands redirected from the transferred nerves to the muscles. Disentangling overlapping signals from EMG recordings remains complex, as they can contain mixed neural information that complicates limb function interpretation. To address this challenge, Regenerative Peripheral Nerve Interfaces (RPNIs) surgically partition the nerve into individual fascicles that reinnervate specific muscle grafts, isolating distinct neural sources for more precise control and interpretation of EMG signals. We introduce a novel biointerface that combines TMR surgery of polyvalent nerves with a high-density micro-electrode array implanted at a single site within a reinnervated muscle. Instead of surgically identifying distinct nerve fascicles, our approach separates all neural signals that are re-directed into a single muscle, using the high spatio-temporal selectivity of the micro-electrode array and mathematical source separation methods. We recorded EMG signals from four reinnervated muscles while volunteers performed phantom limb tasks. The decomposition of these signals into motor unit activity revealed distinct clusters of motor neurons associated with diverse functional tasks. Notably, our method enabled the extraction of multiple neural commands within a single reinnervated muscle, eliminating the need for surgical nerve division. This approach not only has the potential of enhancing prosthesis control but also uncovers mechanisms of motor neuron synergies following TMR, providing valuable insights into how the central nervous system encodes movement after reinnervation.

Recommender systems remain underutilized in humanities and historical research, despite their potential to enhance the discovery of cultural records. This paper offers an initial value identification of the multiple stakeholders that might be impacted by recommendations in Monasterium.net, a digital archive for historical legal documents. Specifically, we discuss the diverse values and objectives of its stakeholders, such as editors, aggregators, platform owners, researchers, publishers, and funding agencies. These in-depth insights into the potentially conflicting values of stakeholder groups allow designing and adapting recommender systems to enhance their usefulness for humanities and historical research. Additionally, our findings will support deeper engagement with additional stakeholders to refine value models and evaluation metrics for recommender systems in the given domains. Our conclusions are embedded in and applicable to other digital archives and a broader cultural heritage context., Comment: To be presented at: NORMalize 2024: The Second Workshop on the Normative Design and Evaluation of Recommender Systems, October 18, 2024, co-located with the ACM Conference on Recommender Systems 2024 (RecSys 2024), Bari, Italy

This study examines the impact of historical text normalization on the classification of medieval charters, specifically focusing on document dating and locating. Using a data set of Middle High German charters from a digital archive, we evaluate various classifiers, including traditional and transformer-based models, with and without normalization. Our results indicate that the given normalization minimally improves locating tasks but reduces accuracy for dating, implying that original texts contain crucial features that normalization may obscure. We find that support vector machines and gradient boosting outperform other models, questioning the efficiency of transformers for this use case. Results suggest a selective approach to historical text normalization, emphasizing the significance of preserving some textual characteristics that are critical for classification tasks in document analysis., Comment: This preprint has not undergone peer review or any post-submission improvements or corrections

Data scarcity is a major limiting factor for applying modern machine learning techniques to clinical tasks. Although sufficient data exists for some well-studied medical tasks, there remains a long tail of clinically relevant tasks with poor data availability. Recently, numerous foundation models have demonstrated high suitability for few-shot learning (FSL) and zero-shot learning (ZSL), potentially making them more accessible to practitioners. However, it remains unclear which foundation model performs best on FSL medical image analysis tasks and what the optimal methods are for learning from limited data. We conducted a comprehensive benchmark study of ZSL and FSL using 16 pretrained foundation models on 19 diverse medical imaging datasets. Our results indicate that BiomedCLIP, a model pretrained exclusively on medical data, performs best on average for very small training set sizes, while very large CLIP models pretrained on LAION-2B perform best with slightly more training samples. However, simply fine-tuning a ResNet-18 pretrained on ImageNet performs similarly with more than five training examples per class. Our findings also highlight the need for further research on foundation models specifically tailored for medical applications and the collection of more datasets to train these models., Comment: Accepted as an oral presentation in MICCAI 2024 2nd International Workshop on Foundation Models for General Medical AI

FOLD-RM is an explainable machine learning classification algorithm that uses training data to create a set of classification rules. In this paper we introduce CON-FOLD which extends FOLD-RM in several ways. CON-FOLD assigns probability-based confidence scores to rules learned for a classification task. This allows users to know how confident they should be in a prediction made by the model. We present a confidence-based pruning algorithm that uses the unique structure of FOLD-RM rules to efficiently prune rules and prevent overfitting. Furthermore, CON-FOLD enables the user to provide pre-existing knowledge in the form of logic program rules that are either (fixed) background knowledge or (modifiable) initial rule candidates. The paper describes our method in detail and reports on practical experiments. We demonstrate the performance of the algorithm on benchmark datasets from the UCI Machine Learning Repository. For that, we introduce a new metric, Inverse Brier Score, to evaluate the accuracy of the produced confidence scores. Finally we apply this extension to a real world example that requires explainability: marking of student responses to a short answer question from the Australian Physics Olympiad.

In this paper we demonstrate how logic programming systems and Automated first-order logic Theorem Provers (ATPs) can improve the accuracy of Large Language Models (LLMs) for logical reasoning tasks where the baseline performance is given by direct LLM solutions. We first evaluate LLM reasoning on steamroller problems using the PRONTOQA benchmark. We show how accuracy can be improved with a neuro-symbolic architecture where the LLM acts solely as a front-end for translating a given problem into a formal logic language and an automated reasoning engine is called for solving it. However, this approach critically hinges on the correctness of the LLM translation. To assess this translation correctness, we secondly define a framework of syntactic and semantic error categories. We implemented the framework and used it to identify errors that LLMs make in the benchmark domain. Based on these findings, we thirdly extended our method with capabilities for automatically correcting syntactic and semantic errors. For semantic error correction we integrate first-order logic ATPs, which is our main and novel contribution. We demonstrate that this approach reduces semantic errors significantly and further increases the accurracy of LLM logical reasoning.

Inverse problems, such as accelerated MRI reconstruction, are ill-posed and an infinite amount of possible and plausible solutions exist. This may not only lead to uncertainty in the reconstructed image but also in downstream tasks such as semantic segmentation. This uncertainty, however, is mostly not analyzed in the literature, even though probabilistic reconstruction models are commonly used. These models can be prone to ignore plausible but unlikely solutions like rare pathologies. Building on MRI reconstruction approaches based on diffusion models, we add guidance to the diffusion process during inference, generating two meaningfully diverse reconstructions corresponding to an upper and lower bound segmentation. The reconstruction uncertainty can then be quantified by the difference between these bounds, which we coin the 'uncertainty boundary'. We analyzed the behavior of the upper and lower bound segmentations for a wide range of acceleration factors and found the uncertainty boundary to be both more reliable and more accurate compared to repeated sampling. Code is available at https://github.com/NikolasMorshuis/SGR, Comment: Accepted at DGM4MICCAI 2024

Reward models (RMs) are crucial for aligning large language models (LLMs) with human preferences. They are trained using preference datasets where each example consists of one input prompt, two responses, and a preference label. As curating a high-quality human labeled preference dataset is both time-consuming and expensive, people often rely on existing powerful LLMs for preference label generation. This can potentially introduce noise and impede RM training. In this work, we present RMBoost, a novel synthetic preference data generation paradigm to boost reward model quality. Unlike traditional methods, which generate two responses before obtaining the preference label, RMBoost first generates one response and selects a preference label, followed by generating the second more (or less) preferred response conditioned on the pre-selected preference label and the first response. This approach offers two main advantages. First, RMBoost reduces labeling noise since preference pairs are constructed intentionally. Second, RMBoost facilitates the creation of more diverse responses by incorporating various quality aspects (e.g., helpfulness, relevance, completeness) into the prompts. We conduct extensive experiments across three diverse datasets and demonstrate that RMBoost outperforms other synthetic preference data generation techniques and significantly boosts the performance of four distinct reward models.

The popularity of automated news headline generation has surged with advancements in pre-trained language models. However, these models often suffer from the ``hallucination'' problem, where the generated headline is not fully supported by its source article. Efforts to address this issue have predominantly focused on English, using over-simplistic classification schemes that overlook nuanced hallucination types. In this study, we introduce the first multilingual, fine-grained news headline hallucination detection dataset that contains over 11 thousand pairs in 5 languages, each annotated with detailed hallucination types by experts. We conduct extensive experiments on this dataset under two settings. First, we implement several supervised fine-tuning approaches as preparatory solutions and demonstrate this dataset's challenges and utilities. Second, we test various large language models' in-context learning abilities and propose two novel techniques, language-dependent demonstration selection and coarse-to-fine prompting, to boost the few-shot hallucination detection performance in terms of the example-F1 metric. We release this dataset to foster further research in multilingual, fine-grained headline hallucination detection.

Recent works have introduced methods to estimate segmentation performance without ground truth, relying solely on neural network softmax outputs. These techniques hold potential for intuitive output quality control. However, such performance estimates rely on calibrated softmax outputs, which is often not the case in modern neural networks. Moreover, the estimates do not take into account inherent uncertainty in segmentation tasks. These limitations may render precise performance predictions unattainable, restricting the practical applicability of performance estimation methods. To address these challenges, we develop a novel approach for predicting performance ranges with statistical guarantees of containing the ground truth with a user specified probability. Our method leverages sampling-based segmentation uncertainty estimation to derive heuristic performance ranges, and applies split conformal prediction to transform these estimates into rigorous prediction ranges that meet the desired guarantees. We demonstrate our approach on the FIVES retinal vessel segmentation dataset and compare five commonly used sampling-based uncertainty estimation techniques. Our results show that it is possible to achieve the desired coverage with small prediction ranges, highlighting the potential of performance range prediction as a valuable tool for output quality control., Comment: Accepted as an oral presentation at MICCAI UNSURE 2024

This study presents the first examination of the ability of Large Language Models (LLMs) to follow reasoning strategies that are used to guide Automated Theorem Provers (ATPs). We evaluate the performance of GPT4, GPT3.5 Turbo and Google's recent Gemini model on problems from a steamroller domain. In addition to determining accuracy we make use of the Natural Language Processing library spaCy to explore new methods of investigating LLM's reasoning capabilities. This led to one alarming result, the low correlation between correct reasoning and correct answers for any of the tested models. We found that the models' performance when using the ATP reasoning strategies was comparable to one-shot chain of thought and observe that attention to uncertainty in the accuracy results is critical when drawing conclusions about model performance. Consistent with previous speculation we confirm that LLMs have a preference for, and are best able to follow, bottom up reasoning processes. However, the reasoning strategies can still be beneficial for deriving small and relevant sets of formulas for external processing by a trusted inference engine.

We present Crab X-ray polarization measurements using IXPE data with a total exposure of 300ks, three times more than the initial 2022 discovery paper. Polarization is detected in three times more pulsar phase bins, revealing an S-shaped $+40^\circ$ polarization angle sweep in the main pulse and ${>}1\sigma$ departures from the OPTIMA optical polarization in both pulses, suggesting different radiation mechanisms or sites for the polarized emission at the two wavebands. Our polarization map of the inner nebula reveals a toroidal magnetic field, as seen in prior IXPE analyses. Along the southern jet, the magnetic field orientation relative to the jet axis changes from perpendicular to parallel and the polarization degree decreases by ${\sim}6\%$. These observations may be explained by kink instabilities along the jet or a collision with a dense, jet-deflecting medium at the tip. Using spectropolarimetric analysis, we find asymmetric polarization in the four quadrants of the inner nebula, as expected for a toroidal field geometry, and a spatial correlation between polarization degree and photon index., Comment: 14 pages, 7 figures, 3 tables. Accepted by The Astrophysical Journal

Deformable image registration is fundamental to many medical imaging applications. Registration is an inherently ambiguous task often admitting many viable solutions. While neural network-based registration techniques enable fast and accurate registration, the majority of existing approaches are not able to estimate uncertainty. Here, we present PULPo, a method for probabilistic deformable registration capable of uncertainty quantification. PULPo probabilistically models the distribution of deformation fields on different hierarchical levels combining them using Laplacian pyramids. This allows our method to model global as well as local aspects of the deformation field. We evaluate our method on two widely used neuroimaging datasets and find that it achieves high registration performance as well as substantially better calibrated uncertainty quantification compared to the current state-of-the-art., Comment: Accepted as full paper to MICCAI 2024

We present multiwavelength polarization measurements of the luminous blazar Mrk~501 over a 14-month period. The 2--8 keV X-ray polarization was measured with the Imaging X-ray Polarimetry Explorer (IXPE) with six 100-ks observations spanning from 2022 March to 2023 April. Each IXPE observation was accompanied by simultaneous X-ray data from NuSTAR, Swift/XRT, and/or XMM-Newton. Complementary optical-infrared polarization measurements were also available in the B, V, R, I, and J bands, as were radio polarization measurements from 4.85 GHz to 225.5 GHz. Among the first five IXPE observations, we did not find significant variability in the X-ray polarization degree and angle with IXPE. However, the most recent sixth observation found an elevated polarization degree at $>3\sigma$ above the average of the other five observations. The optical and radio measurements show no apparent correlations with the X-ray polarization properties. Throughout the six IXPE observations, the X-ray polarization degree remained higher than, or similar to, the R-band optical polarization degree, which remained higher than the radio value. This is consistent with the energy-stratified shock scenario proposed to explain the first two IXPE observations, in which the polarized X-ray, optical, and radio emission arises from different regions., Comment: Accepted for publication in ApJ

Cancer remains a leading cause of death, highlighting the importance of effective radiotherapy (RT). Magnetic resonance-guided linear accelerators (MR-Linacs) enable imaging during RT, allowing for inter-fraction, and perhaps even intra-fraction, adjustments of treatment plans. However, achieving this requires fast and accurate dose calculations. While Monte Carlo simulations offer accuracy, they are computationally intensive. Deep learning frameworks show promise, yet lack uncertainty quantification crucial for high-risk applications like RT. Risk-controlling prediction sets (RCPS) offer model-agnostic uncertainty quantification with mathematical guarantees. However, we show that naive application of RCPS may lead to only certain subgroups such as the image background being risk-controlled. In this work, we extend RCPS to provide prediction intervals with coverage guarantees for multiple subgroups with unknown subgroup membership at test time. We evaluate our algorithm on real clinical planing volumes from five different anatomical regions and show that our novel subgroup RCPS (SG-RCPS) algorithm leads to prediction intervals that jointly control the risk for multiple subgroups. In particular, our method controls the risk of the crucial voxels along the radiation beam significantly better than conventional RCPS., Comment: This work was accepted as a full paper at MICCAI 2024

The Robertson model describing a chemical reaction involving three reactants is one of the classical examples of stiffness in ODEs. The stiffness is caused by the occurrence of three reaction rates $k_1,\,k_2$, and $k_3$, with largely differing orders of magnitude, acting as parameters. The model has been widely used as a numerical test problem. Surprisingly, no asymptotic analysis of this multiscale problem seems to exist. In this paper we provide a full asymptotic analysis of the Robertson model under the assumption $k_1, k_3 \ll k_2$. We rewrite the equations as a two-parameter singular perturbation problem in the rescaled small parameters $(\varepsilon_1,\varepsilon_2):=(k_1/k_2,k_3/k_2)$, which we then analyze using geometric singular perturbation theory (GSPT). To deal with the multi-parameter singular structure, we perform blow-ups in parameter- and variable space. We identify four distinct regimes in a neighbourhood of the singular limit $(\varepsilon_1,\varepsilon_2)= (0,0)$. Within these four regimes we use GSPT and additional blow-ups to analyze the dynamics and the structure of solutions. Our asymptotic results are in excellent qualitative and quantitative agreement with the numerics., Comment: Updated the introduction and made some minor adjustments

Selective Classification, wherein models can reject low-confidence predictions, promises reliable translation of machine-learning based classification systems to real-world scenarios such as clinical diagnostics. While current evaluation of these systems typically assumes fixed working points based on pre-defined rejection thresholds, methodological progress requires benchmarking the general performance of systems akin to the $\mathrm{AUROC}$ in standard classification. In this work, we define 5 requirements for multi-threshold metrics in selective classification regarding task alignment, interpretability, and flexibility, and show how current approaches fail to meet them. We propose the Area under the Generalized Risk Coverage curve ($\mathrm{AUGRC}$), which meets all requirements and can be directly interpreted as the average risk of undetected failures. We empirically demonstrate the relevance of $\mathrm{AUGRC}$ on a comprehensive benchmark spanning 6 data sets and 13 confidence scoring functions. We find that the proposed metric substantially changes metric rankings on 5 out of the 6 data sets.