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Defacing is often applied to head magnetic resonance image (MRI) datasets prior to public release to address privacy concerns. The alteration of facial and nearby voxels has provoked discussions about the true capability of these techniques to ensure privacy as well as their impact on downstream tasks. With advancements in deep generative models, the extent to which defacing can protect privacy is uncertain. Additionally, while the altered voxels are known to contain valuable anatomical information, their potential to support research beyond the anatomical regions directly affected by defacing remains uncertain. To evaluate these considerations, we develop a refacing pipeline that recovers faces in defaced head MRIs using cascaded diffusion probabilistic models (DPMs). The DPMs are trained on images from 180 subjects and tested on images from 484 unseen subjects, 469 of whom are from a different dataset. To assess whether the altered voxels in defacing contain universally useful information, we also predict computed tomography (CT)-derived skeletal muscle radiodensity from facial voxels in both defaced and original MRIs. The results show that DPMs can generate high-fidelity faces that resemble the original faces from defaced images, with surface distances to the original faces significantly smaller than those of a population average face (p < 0.05). This performance also generalizes well to previously unseen datasets. For skeletal muscle radiodensity predictions, using defaced images results in significantly weaker Spearman's rank correlation coefficients compared to using original images (p < 10-4). For shin muscle, the correlation is statistically significant (p < 0.05) when using original images but not statistically significant (p > 0.05) when any defacing method is applied, suggesting that defacing might not only fail to protect privacy but also eliminate valuable information.

Prior research on training grounded factuality classification models to detect hallucinations in large language models (LLMs) has relied on public natural language inference (NLI) data and synthetic data. However, conventional NLI datasets are not well-suited for document-level reasoning, which is critical for detecting LLM hallucinations. Recent approaches to document-level synthetic data generation involve iteratively removing sentences from documents and annotating factuality using LLM-based prompts. While effective, this method is computationally expensive for long documents and limited by the LLM's capabilities. In this work, we analyze the differences between existing synthetic training data used in state-of-the-art models and real LLM output claims. Based on our findings, we propose a novel approach for synthetic data generation, CG2C, that leverages multi-hop reasoning on context graphs extracted from documents. Our fact checker model, FactCG, demonstrates improved performance with more connected reasoning, using the same backbone models. Experiments show it even outperforms GPT-4-o on the LLM-Aggrefact benchmark with much smaller model size., Comment: NAACL 2025

Background: When developing a clinical prediction model using time-to-event data, previous research focuses on the sample size to minimise overfitting and precisely estimate the overall risk. However, instability of individual-level risk estimates may still be large. Methods: We propose a decomposition of Fisher's information matrix to examine and calculate the sample size required for developing a model that aims for precise and fair risk estimates. We propose a six-step process which can be used before data collection or when an existing dataset is available. Steps (1) to (5) require researchers to specify the overall risk in the target population at a key time-point of interest; an assumed pragmatic 'core model' in the form of an exponential regression model; the (anticipated) joint distribution of core predictors included in that model; and the distribution of any censoring. Results: We derive closed-form solutions that decompose the variance of an individual's estimated event rate into Fisher's unit information matrix, predictor values and total sample size; this allows researchers to calculate and examine uncertainty distributions around individual risk estimates and misclassification probabilities for specified sample sizes. We provide an illustrative example in breast cancer and emphasise the importance of clinical context, including risk thresholds for decision making, and examine fairness concerns for pre- and post-menopausal women. Lastly, in two empirical evaluations, we provide reassurance that uncertainty interval widths based on our approach are close to using more flexible models. Conclusions: Our approach allows users to identify the (target) sample size required to develop a prediction model for time-to-event outcomes, via the pmstabilityss module. It aims to facilitate models with improved trust, reliability and fairness in individual-level predictions., Comment: arXiv admin note: text overlap with arXiv:2407.09293

Diffusion-weighted Magnetic Resonance Imaging (dMRI) is an essential tool in neuroimaging. It is arguably the sole noninvasive technique for examining the microstructural properties and structural connectivity of the brain. Recent years have seen the emergence of machine learning and data-driven approaches that enhance the speed, accuracy, and consistency of dMRI data analysis. However, traditional deep learning models often fell short, as they typically utilize pixel-level or volumetric patch-level embeddings similar to those used in structural MRI, and do not account for the unique distribution of various gradient encodings. In this paper, we propose a novel method called Polyhedra Encoding Transformer (PE-Transformer) for dMRI, designed specifically to handle spherical signals. Our approach involves projecting an icosahedral polygon onto a unit sphere to resample signals from predetermined directions. These resampled signals are then transformed into embeddings, which are processed by a transformer encoder that incorporates orientational information reflective of the icosahedral structure. Through experimental validation with various gradient encoding protocols, our method demonstrates superior accuracy in estimating multi-compartment models and Fiber Orientation Distributions (FOD), outperforming both conventional CNN architectures and standard transformers.

We consider quenched critical percolation on a supercritical Galton--Watson tree with either finite variance or $\alpha$-stable offspring tails for some $\alpha \in (1,2)$. We show that the GHP scaling limit of a quenched critical percolation cluster on this tree is the corresponding $\alpha$-stable tree, as is the case in the annealed setting. As a corollary we obtain that a simple random walk on the cluster also rescales to Brownian motion on the stable tree. Along the way, we also obtain quenched asymptotics for the tail of the cluster size, which completes earlier results obtained in Michelen (2019) and Archer-Vogel (2024).

We present LionsOS, an operating system for security- and safety-critical embedded systems. LionsOS is based on the formally verified seL4 microkernel and designed with verification in mind. It uses a static architecture and features a highly modular design driven by strict separation of concerns and a focus on simplicity. We demonstrate that LionsOS outperforms Linux., Comment: 14 pages, 13 figures

Multi-component liquid mixtures can be both complex and fascinating, with some systems being amenable to simple experimentation at home, giving valuable insight into fundamental aspects of bulk and interfacial phase behaviour. One particularly interesting mixture is the popular drink ouzo, which has charmed both the general public and scientists by virtue of its ability to display spontaneous emulsification when water is added. When these two clear (and potable) liquids are poured into each other, a single milky-coloured liquid is formed. In previous work [Archer et al., Soft Matter 20, 5889 (2024)], the equilibrium phase-diagram for the stable liquid phases of ouzo was captured via experiment and modelling. Here we consider the case when the two liquid phases also coexist with the vapour phase (i.e. along a line of triple points) and within our model uncover the complex bulk phase behaviour for this simple beverage. As a consequence, this leads to some interesting observations, that also apply more widely, about visualising phase diagrams in ternary systems of this type. We also examine the interfacial behaviour, connecting microscopic density functional theory results with macroscopic (Neumann) predictions for the shape of droplets at interfaces.

Shallow permutations were defined in 1977 to be those that satisfy the lower bound of the Diaconis-Graham inequality. Recently, there has been renewed interest in these permutations. In particular, Berman and Tenner showed they satisfy certain pattern avoidance conditions in their cycle form and Woo showed they are exactly those whose cycle diagrams are unlinked. Shallow permutations that avoid 321 have appeared in many contexts; they are those permutations for which depth equals the reflection length, they have unimodal cycles, and they have been called Boolean permutations. Motivated by this interest in 321-avoiding shallow permutations, we investigate $\sigma$-avoiding shallow permutations for all $\sigma \in \mathcal{S}_3$. To do this, we develop more general structural results about shallow permutations, and apply them to enumerate shallow permutations avoiding any pattern of length 3., Comment: 23 pages; added additional citations in v2

Let $T_m(N,2k)$ denote the $m$-th Hecke operator on the space $S_{2k}(\Gamma_0(N))$ of cuspidal modular forms of weight $2k$ and level $N$. In this paper, we study the non-repetition of the second coefficient of the characteristic polynomial of $T_m(N,2k)$. We obtain results in the horizontal aspect (where $m$ varies), the vertical aspect (where $k$ varies), and the level aspect (where $N$ varies). Finally, we use these non-repetition results to extend a result of Vilardi and Xue on distinguishing Hecke eigenforms., Comment: 22 pages

In recent years, it has become increasingly clear that space weather disturbances can be triggered by transient upstream mesoscale structures (TUMS), independently of the occurrence of large-scale solar wind (SW) structures, such as interplanetary coronal mass ejections and stream interaction regions. Different types of magnetospheric pulsations, transient perturbations of the geomagnetic field and auroral structures are often observed during times when SW monitors indicate quiet conditions, and have been found to be associated to TUMS. In this mini-review we describe the space weather phenomena that have been associated with four of the largest-scale and the most energetic TUMS, namely hot flow anomalies, foreshock bubbles, travelling foreshocks and foreshock compressional boundaries. The space weather phenomena associated with TUMS tend to be more localized and less intense compared to geomagnetic storms. However, the quiet time space weather may occur more often since, especially during solar minima, quiet SW periods prevail over the perturbed times., Comment: 1 figure, 1 table

In causal inference, an important problem is to quantify the effects of interventions or treatments. Many studies focus on estimating the mean causal effects; however, these estimands may offer limited insight since two distributions can share the same mean yet exhibit significant differences. Examining the causal effects from a distributional perspective provides a more thorough understanding. In this paper, we employ a semiparametric density ratio model (DRM) to characterize the counterfactual distributions, introducing a framework that assumes a latent structure shared by these distributions. Our model offers flexibility by avoiding strict parametric assumptions on the counterfactual distributions. Specifically, the DRM incorporates a nonparametric component that can be estimated through the method of empirical likelihood (EL), using the data from all the groups stemming from multiple interventions. Consequently, the EL-DRM framework enables inference of the counterfactual distribution functions and their functionals, facilitating direct and transparent causal inference from a distributional perspective. Numerical studies on both synthetic and real-world data validate the effectiveness of our approach.

Estimated brain age from magnetic resonance image (MRI) and its deviation from chronological age can provide early insights into potential neurodegenerative diseases, supporting early detection and implementation of prevention strategies. Diffusion MRI (dMRI), a widely used modality for brain age estimation, presents an opportunity to build an earlier biomarker for neurodegenerative disease prediction because it captures subtle microstructural changes that precede more perceptible macrostructural changes. However, the coexistence of macro- and micro-structural information in dMRI raises the question of whether current dMRI-based brain age estimation models are leveraging the intended microstructural information or if they inadvertently rely on the macrostructural information. To develop a microstructure-specific brain age, we propose a method for brain age identification from dMRI that minimizes the model's use of macrostructural information by non-rigidly registering all images to a standard template. Imaging data from 13,398 participants across 12 datasets were used for the training and evaluation. We compare our brain age models, trained with and without macrostructural information minimized, with an architecturally similar T1-weighted (T1w) MRI-based brain age model and two state-of-the-art T1w MRI-based brain age models that primarily use macrostructural information. We observe difference between our dMRI-based brain age and T1w MRI-based brain age across stages of neurodegeneration, with dMRI-based brain age being older than T1w MRI-based brain age in participants transitioning from cognitively normal (CN) to mild cognitive impairment (MCI), but younger in participants already diagnosed with Alzheimer's disease (AD). Approximately 4 years before MCI diagnosis, dMRI-based brain age yields better performance than T1w MRI-based brain ages in predicting transition from CN to MCI.

Simultaneous space-time focusing (SSTF) is sometimes claimed to reduce the longitudinal extent of the high-intensity region near the focus, in contradiction to the original work on this topic. Here we seek to address this confusion by using numerical and analytical methods to investigate the degree of localisation of the spatio-temporal intensity of an SSTF pulse. The analytical method is found to be in excellent agreement with numerical calculations and yields, for bi-Gaussian input pulses, expressions for the three-dimensional spatio-temporal intensity profile of the SSTF pulse, and for the on-axis bandwidth, pulse duration, and pulse-front tilt (PFT) of the SSTF pulse. To provide further insight, we propose a method for determining the transverse input profile of a non-SSTF pulse with equivalent spatial focusing. We find that the longitudinal variations of the peak axial intensities of the SSTF and spatially equivalent (SE) pulses are the same, apart from a constant factor, and hence that SSTF does not constrain the region of high intensity more than a non-SSTF pulse with equivalent focusing. We demonstrate that one possible cause of confusion in the literature arises from the fact that a simplistic method for calculating the pulse intensity exaggerates the degree of intensity localisation, unless the spatio-temporal couplings inherent to SSTF pulses are accounted for.

Proper quality control (QC) is time consuming when working with large-scale medical imaging datasets, yet necessary, as poor-quality data can lead to erroneous conclusions or poorly trained machine learning models. Most efforts to reduce data QC time rely on outlier detection, which cannot capture every instance of algorithm failure. Thus, there is a need to visually inspect every output of data processing pipelines in a scalable manner. We design a QC pipeline that allows for low time cost and effort across a team setting for a large database of diffusion weighted and structural magnetic resonance images. Our proposed method satisfies the following design criteria: 1.) a consistent way to perform and manage quality control across a team of researchers, 2.) quick visualization of preprocessed data that minimizes the effort and time spent on the QC process without compromising the condition or caliber of the QC, and 3.) a way to aggregate QC results across pipelines and datasets that can be easily shared. In addition to meeting these design criteria, we also provide information on what a successful output should be and common occurrences of algorithm failures for various processing pipelines. Our method reduces the time spent on QC by a factor of over 20 when compared to naively opening outputs in an image viewer and demonstrate how it can facilitate aggregation and sharing of QC results within a team. While researchers must spend time on robust visual QC of data, there are mechanisms by which the process can be streamlined and efficient., Comment: 22 pages, 12 figures, 1 table, 6 supplemental figures

An incomplete field-of-view (FOV) in diffusion magnetic resonance imaging (dMRI) can severely hinder the volumetric and bundle analyses of whole-brain white matter connectivity. Although existing works have investigated imputing the missing regions using deep generative models, it remains unclear how to specifically utilize additional information from paired multi-modality data and whether this can enhance the imputation quality and be useful for downstream tractography. To fill this gap, we propose a novel framework for imputing dMRI scans in the incomplete part of the FOV by integrating the learned diffusion features in the acquired part of the FOV to the complete brain anatomical structure. We hypothesize that by this design the proposed framework can enhance the imputation performance of the dMRI scans and therefore be useful for repairing whole-brain tractography in corrupted dMRI scans with incomplete FOV. We tested our framework on two cohorts from different sites with a total of 96 subjects and compared it with a baseline imputation method that treats the information from T1w and dMRI scans equally. The proposed framework achieved significant improvements in imputation performance, as demonstrated by angular correlation coefficient (p < 1E-5), and in downstream tractography accuracy, as demonstrated by Dice score (p < 0.01). Results suggest that the proposed framework improved imputation performance in dMRI scans by specifically utilizing additional information from paired multi-modality data, compared with the baseline method. The imputation achieved by the proposed framework enhances whole brain tractography, and therefore reduces the uncertainty when analyzing bundles associated with neurodegenerative., Comment: 20 pages; 8 figures

We investigate the phase ordering (pattern formation) of systems of two-dimensional core-shell particles using Monte-Carlo (MC) computer simulations and classical density functional theory (DFT). The particles interact via a pair potential having a hard core and a repulsive square shoulder. Our simulations show that on cooling, the liquid state structure becomes increasingly characterised by long wavelength density modulations, and on further cooling forms a variety of other phases, including clustered, striped and other patterned phases. In DFT, the hard core part of the potential is treated using either fundamental measure theory or a simple local density approximation, whereas the soft shoulder is treated using the random phase approximation. The different DFTs are bench-marked using large-scale grand-canonical-MC and Gibbs-ensemble-MC simulations, demonstrating their predictive capabilities and shortcomings. We find that having the liquid state static structure factor $S(k)$ for wavenumber $k$ is sufficient to identify the Fourier modes governing both the liquid and solid phases. This allows to identify from easier-to-obtain liquid state data the wavenumbers relevant to the periodic phases and to predict roughly where in the phase diagram these patterned phases arise., Comment: 42 pages, 9 figures

In this paper, we consider cyclic permutations that avoid the monotone decreasing permutation $k(k-1)\ldots 21$, whose cycle also demonstrates some pattern avoidance. If the cycle is written in standard form with 1 appearing at the beginning of the cycle and the standard form avoids a pattern of length 3, we find answers in terms of continued fraction generating functions. We also consider the case that every cyclic rotation of the cycle form of the permutation avoids a pattern of length 4 and enumerate two such cases.

Curating, processing, and combining large-scale medical imaging datasets from national studies is a non-trivial task due to the intense computation and data throughput required, variability of acquired data, and associated financial overhead. Existing platforms or tools for large-scale data curation, processing, and storage have difficulty achieving a viable cost-to-scale ratio of computation speed for research purposes, either being too slow or too expensive. Additionally, management and consistency of processing large data in a team-driven manner is a non-trivial task. We design a BIDS-compliant method for an efficient and robust data processing pipeline of large-scale diffusion-weighted and T1-weighted MRI data compatible with low-cost, high-efficiency computing systems. Our method accomplishes automated querying of data available for processing and process running in a consistent and reproducible manner that has long-term stability, while using heterogenous low-cost computational resources and storage systems for efficient processing and data transfer. We demonstrate how our organizational structure permits efficiency in a semi-automated data processing pipeline and show how our method is comparable in processing time to cloud-based computation while being almost 20 times more cost-effective. Our design allows for fast data throughput speeds and low latency to reduce the time for data transfer between storage servers and computation servers, achieving an average of 0.60 Gb/s compared to 0.33 Gb/s for using cloud-based processing methods. The design of our workflow engine permits quick process running while maintaining flexibility to adapt to newly acquired data.

To date, there has been no comprehensive study characterizing the effect of diffusion-weighted magnetic resonance imaging voxel resolution on the resulting connectome for high resolution subject data. Similarity in results improved with higher resolution, even after initial down-sampling. To ensure robust tractography and connectomes, resample data to 1 mm isotropic resolution.

In February 2017, the blazar OJ~287 underwent a period of intense multiwavelength activity. It reached a new historic peak in the soft X-ray (0.3-10 keV) band, as measured by Swift-XRT. This event coincides with a very-high-energy (VHE) $\gamma$-ray outburst that led VERITAS to detect emission above 100 GeV, with a detection significance of $10\sigma$ (from 2016 December 9 to 2017 March 31). The time-averaged VHE $\gamma$-ray spectrum was consistent with a soft power law ($\Gamma = -3.81 \pm 0.26$) and an integral flux corresponding to $\sim2.4\%$ that of the Crab Nebula above the same energy. Contemporaneous data from multiple instruments across the electromagnetic spectrum reveal complex flaring behavior, primarily in the soft X-ray and VHE bands. To investigate the possible origin of such an event, our study focuses on three distinct activity states: before, during, and after the February 2017 peak. The spectral energy distributions during these periods suggest the presence of at least two non-thermal emission zones, with the more compact one responsible for the observed flare. Broadband modeling results and observations of a new radio knot in the jet of OJ~287 in 2017 are consistent with a flare originating from a strong recollimation shock outside the radio core., Comment: 21 pages, 7 figures, accepted for publication in The Astrophysical Journal

When developing a clinical prediction model, the sample size of the development dataset is a key consideration. Small sample sizes lead to greater concerns of overfitting, instability, poor performance and lack of fairness. Previous research has outlined minimum sample size calculations to minimise overfitting and precisely estimate the overall risk. However even when meeting these criteria, the uncertainty (instability) in individual-level risk estimates may be considerable. In this article we propose how to examine and calculate the sample size required for developing a model with acceptably precise individual-level risk estimates to inform decisions and improve fairness. We outline a five-step process to be used before data collection or when an existing dataset is available. It requires researchers to specify the overall risk in the target population, the (anticipated) distribution of key predictors in the model, and an assumed 'core model' either specified directly (i.e., a logistic regression equation is provided) or based on specified C-statistic and relative effects of (standardised) predictors. We produce closed-form solutions that decompose the variance of an individual's risk estimate into Fisher's unit information matrix, predictor values and total sample size; this allows researchers to quickly calculate and examine individual-level uncertainty interval widths and classification instability for specified sample sizes. Such information can be presented to key stakeholders (e.g., health professionals, patients, funders) using prediction and classification instability plots to help identify the (target) sample size required to improve trust, reliability and fairness in individual predictions. Our proposal is implemented in software module pmstabilityss. We provide real examples and emphasise the importance of clinical context including any risk thresholds for decision making., Comment: 36 pages, 6 figures, 1 table

The fundamental bijection is a bijection $\theta:\mathcal{S}_n\to\mathcal{S}_n$ in which one uses the standard cycle form of one permutation to obtain another permutation in one-line form. In this paper, we enumerate the set of permutations $\pi \in \mathcal{S}_n$ that avoids a pattern $\sigma \in \mathcal{S}_3$, whose image $\theta(\pi)$ also avoids $\sigma$. We additionally consider what happens under repeated iterations of $\theta$; in particular, we enumerate permutations $\pi \in \mathcal{S}_n$ that have the property that $\pi$ and its first $k$ iterations under $\theta$ all avoid a pattern $\sigma$. Finally, we consider permutations with the property that $\pi=\theta^2(\pi)$ that avoid a given pattern $\sigma$, and end the paper with some directions for future study., Comment: 21 pages

When evaluating the performance of a model for individualised risk prediction, the sample size needs to be large enough to precisely estimate the performance measures of interest. Current sample size guidance is based on precisely estimating calibration, discrimination, and net benefit, which should be the first stage of calculating the minimum required sample size. However, when a clinically important threshold is used for classification, other performance measures can also be used. We extend the previously published guidance to precisely estimate threshold-based performance measures. We have developed closed-form solutions to estimate the sample size required to target sufficiently precise estimates of accuracy, specificity, sensitivity, PPV, NPV, and F1-score in an external evaluation study of a prediction model with a binary outcome. This approach requires the user to pre-specify the target standard error and the expected value for each performance measure. We describe how the sample size formulae were derived and demonstrate their use in an example. Extension to time-to-event outcomes is also considered. In our examples, the minimum sample size required was lower than that required to precisely estimate the calibration slope, and we expect this would most often be the case. Our formulae, along with corresponding Python code and updated R and Stata commands (pmvalsampsize), enable researchers to calculate the minimum sample size needed to precisely estimate threshold-based performance measures in an external evaluation study. These criteria should be used alongside previously published criteria to precisely estimate the calibration, discrimination, and net-benefit., Comment: 27 pages, 1 figure

We consider a few special cases of the more general question: How many permutations $\pi\in\mathcal{S}_n$ have the property that $\pi^2$ has $j$ descents for some $j$? In this paper, we first enumerate Grassmannian permutations $\pi$ by the number of descents in $\pi^2$. We then consider all permutations whose square has exactly one descent, fully enumerating when the descent is "small" and providing a lower bound in the general case. Finally, we enumerate permutations whose square or cube has the maximum number of descents, and finish the paper with a few future directions for study.